E_i

PCDBTRF()

calculate the update block for previous proc, E_i = gl_i{gu_i

PCDTTRF()

calculate the update block for previous proc, E_i = gl_i{gu_i

PCPBTRF()

calculate the update block for previous proc, E_i = g_i{g_i}^

PCPTTRF()

calculate the update block for previous proc, E_i = g_i{g_i}^

PDDBTRF()

calculate the update block for previous proc, E_i = gl_i{gu_i

PDDTTRF()

calculate the update block for previous proc, E_i = gl_i{gu_i

PDPBTRF()

calculate the update block for previous proc, E_i = g_i{g_i}^

PDPTTRF()

calculate the update block for previous proc, E_i = g_i{g_i}^

PSDBTRF()

calculate the update block for previous proc, E_i = gl_i{gu_i

PSDTTRF()

calculate the update block for previous proc, E_i = gl_i{gu_i

PSPBTRF()

calculate the update block for previous proc, E_i = g_i{g_i}^

PSPTTRF()

calculate the update block for previous proc, E_i = g_i{g_i}^

PZDBTRF()

calculate the update block for previous proc, E_i = gl_i{gu_i

PZDTTRF()

calculate the update block for previous proc, E_i = gl_i{gu_i

PZPBTRF()

calculate the update block for previous proc, E_i = g_i{g_i}^

PZPTTRF()

calculate the update block for previous proc, E_i = g_i{g_i}^

each

CLAHQR2()

the main loop begins here. i is the loop index and decreases from
ihi to ilo in steps of 1 or 2. each iteration of the loop work
eigenvalues i+1 to ihi have already converged. either l = ilo, or

DSTEQR2()

determine where the matrix splits and choose ql or qr iteration
for each block, according to whether top or bottom diagona

PCDBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*max(bwl,bwu)

PCDBTRF()

number of columns in each processo

PCDBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*max(bwl,bwu)

PCDBTRSV()

number of columns in each processo

PCDTSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PCDTTRF()

number of columns in each processo

PCDTTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PCDTTRSV()

number of columns in each processo

PCGBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= (bwl+bwu)+1

PCGBTRF()

number of columns in each processo

PCGBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= (bwl+bwu)+1

PCGEBD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGEBRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGECON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGEEQU()

the column scale factors, chosen to try to make the largest entry in
each row and column of the distributed matrix b with element

PCGEHD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGEHRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGELQ2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGELQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGELS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGEQL2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGEQLF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGEQPF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGEQR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGEQRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGERFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGERQ2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGERQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGESV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGESVD()

=====
each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGESVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGETF2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGETRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGETRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGETRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGGQRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCGGRQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCHEEV()

=====
a description vector is associated with each 2d block-cyclicly dis
establish the mapping between a matrix entry and its corresponding

PCHEEVD()

query is assumed; the routine calculates the size for all
work arrays. each of these values is returned in the firs
is issued by pxerbla.

PCHEEVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCHEGS2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCHEGST()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCHEGVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCHENGST()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCHENTRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCHETD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCHETRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCHETTRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding

PCLABRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLACGV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLACON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLACONSB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLACP2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLACP3()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLACPY()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLAEVSWP()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLAHQR()

the main loop begins here. i is the loop index and decreases from
ihi to ilo in steps of our schur block size (<=2*iblk). each
and columns l to i.   eigenvalues i+1 to ihi have already

PCLAHRD()

each h(i) has the for
h(i) = i - tau * v * v'

PCLANGE()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLAPIV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLAPV2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLAQGE()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLAQSY()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLARFB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLARFG()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLARFT()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLARZB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLARZT()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLASCL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLASE2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLASET()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLASMSUB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLASSQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLASWP()

the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1).  one
interchange is initiated for each of rows or columns k1 trough k2 o
already been broadcast along the process row or column.

PCLATRA()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLATRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLATRZ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLATTRS()

compute the 1-norm of each column, not including the diagonal

PCLAUU2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLAUUM()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCLAWIL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCMAX1()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCPBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*bw

PCPBTRF()

number of columns in each processo

PCPBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*bw

PCPBTRSV()

number of columns in each processo

PCPOCON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCPOEQU()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCPORFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCPOSV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCPOSVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCPOTF2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCPOTRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCPOTRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCPOTRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCPTSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PCPTTRF()

number of columns in each processo

PCPTTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PCPTTRSV()

number of columns in each processo

PCSRSCL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCSTEIN()

process. pcstein decides on the allocation of work among the
processes and then calls sstein2 (modified lapack routine) on each
expected orthogonalization may not be done.

PCTRCON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCTREVC()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCTRRFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCTRTI2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCTRTRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCTRTRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCTZRZF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNG2L()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNG2R()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNGL2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNGLQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNGQL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNGQR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNGR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNGRQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNM2L()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNM2R()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNMBR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNMHR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNML2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNMLQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNMQL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNMQR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNMR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNMR3()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNMRQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNMRZ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PCUNMTR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDDBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*max(bwl,bwu)

PDDBTRF()

number of columns in each processo

PDDBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*max(bwl,bwu)

PDDBTRSV()

number of columns in each processo

PDDTSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PDDTTRF()

number of columns in each processo

PDDTTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PDDTTRSV()

number of columns in each processo

PDGBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= (bwl+bwu)+1

PDGBTRF()

number of columns in each processo

PDGBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= (bwl+bwu)+1

PDGEBD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGEBRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGECON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGEEQU()

the column scale factors, chosen to try to make the largest entry in
each row and column of the distributed matrix b with element

PDGEHD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGEHRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGELQ2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGELQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGELS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGEQL2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGEQLF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGEQPF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGEQR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGEQRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGERFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGERQ2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGERQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGESV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGESVD()

=====
each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGESVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGETF2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGETRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGETRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGETRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGGQRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDGGRQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLABAD()

pdlabad takes as input the values computed by pdlamch for underflow
and overflow, and returns the square root of each of these values i
to identify machines with a large exponent range, such as the crays,

PDLABRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLACON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLACONSB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLACP2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLACP3()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLACPY()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLAED1()

when there are multiple eigenvalues or if there is a zero in
the z vector.  for each such occurence the dimension of th
performed by the routine pdlaed2.

PDLAED2()

eigenvalues are close together or if there is a tiny entry in the
z vector.  for each such occurrence the order of the related secula

PDLAEVSWP()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLAHQR()

the main loop begins here. i is the loop index and decreases from
ihi to ilo in steps of our schur block size (<=2*iblk). each
and columns l to i.   eigenvalues i+1 to ihi have already

PDLAHRD()

each h(i) has the for
h(i) = i - tau * v * v'

PDLANGE()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLAPIV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLAPV2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLAQGE()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLAQSY()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLARED1D()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLARED2D()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLARFB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLARFG()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLARFT()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLARZB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLARZT()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLASCL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLASE2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLASET()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLASMSUB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLASSQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLASWP()

the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1).  one
interchange is initiated for each of rows or columns k1 trough k2 o
already been broadcast along the process row or column.

PDLATRA()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLATRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLATRZ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLAUU2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLAUUM()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDLAWIL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORG2L()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORG2R()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORGL2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORGLQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORGQL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORGQR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORGR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORGRQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORM2L()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORM2R()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORMBR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORMHR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORML2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORMLQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORMQL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORMQR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORMR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORMR3()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORMRQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORMRZ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDORMTR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDPBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*bw

PDPBTRF()

number of columns in each processo

PDPBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*bw

PDPBTRSV()

number of columns in each processo

PDPOCON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDPOEQU()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDPORFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDPOSV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDPOSVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDPOTF2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDPOTRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDPOTRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDPOTRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDPTSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PDPTTRF()

number of columns in each processo

PDPTTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PDPTTRSV()

number of columns in each processo

PDRSCL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDSTEBZ()

iblock  (global output) integer array, dimension (n)
at each row/column j where e(j) is zero or small, th
matrix.  on exit iblock(i) specifies which block (from 1

PDSTEIN()

process. pdstein decides on the allocation of work among the
processes and then calls dstein2 (modified lapack routine) on each
expected orthogonalization may not be done.

PDSYEV()

=====
a description vector is associated with each 2d block-cyclicly dis
establish the mapping between a matrix entry and its corresponding

PDSYEVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDSYGS2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDSYGST()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDSYGVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDSYNGST()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDSYNTRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDSYTD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDSYTRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDSYTTRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding

PDTRCON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDTRRFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDTRTI2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDTRTRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDTRTRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDTZRZF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PDZSUM1()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PJLAENV()

in particular, the panel blocking factor can be different
on each processor and hence pjlaenv can return differen

PSCSUM1()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSDBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*max(bwl,bwu)

PSDBTRF()

number of columns in each processo

PSDBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*max(bwl,bwu)

PSDBTRSV()

number of columns in each processo

PSDTSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PSDTTRF()

number of columns in each processo

PSDTTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PSDTTRSV()

number of columns in each processo

PSGBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= (bwl+bwu)+1

PSGBTRF()

number of columns in each processo

PSGBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= (bwl+bwu)+1

PSGEBD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGEBRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGECON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGEEQU()

the column scale factors, chosen to try to make the largest entry in
each row and column of the distributed matrix b with element

PSGEHD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGEHRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGELQ2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGELQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGELS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGEQL2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGEQLF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGEQPF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGEQR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGEQRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGERFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGERQ2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGERQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGESV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGESVD()

=====
each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGESVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGETF2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGETRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGETRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGETRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGGQRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSGGRQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLABAD()

pslabad takes as input the values computed by pslamch for underflow
and overflow, and returns the square root of each of these values i
to identify machines with a large exponent range, such as the crays,

PSLABRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLACON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLACONSB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLACP2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLACP3()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLACPY()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLAED1()

when there are multiple eigenvalues or if there is a zero in
the z vector.  for each such occurence the dimension of th
performed by the routine pslaed2.

PSLAED2()

eigenvalues are close together or if there is a tiny entry in the
z vector.  for each such occurrence the order of the related secula

PSLAEVSWP()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLAHQR()

the main loop begins here. i is the loop index and decreases from
ihi to ilo in steps of our schur block size (<=2*iblk). each
and columns l to i.   eigenvalues i+1 to ihi have already

PSLAHRD()

each h(i) has the for
h(i) = i - tau * v * v'

PSLANGE()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLAPIV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLAPV2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLAQGE()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLAQSY()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLARED1D()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLARED2D()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLARFB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLARFG()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLARFT()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLARZB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLARZT()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLASCL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLASE2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLASET()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLASMSUB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLASSQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLASWP()

the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1).  one
interchange is initiated for each of rows or columns k1 trough k2 o
already been broadcast along the process row or column.

PSLATRA()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLATRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLATRZ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLAUU2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLAUUM()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSLAWIL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORG2L()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORG2R()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORGL2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORGLQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORGQL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORGQR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORGR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORGRQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORM2L()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORM2R()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORMBR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORMHR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORML2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORMLQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORMQL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORMQR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORMR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORMR3()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORMRQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORMRZ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSORMTR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSPBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*bw

PSPBTRF()

number of columns in each processo

PSPBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*bw

PSPBTRSV()

number of columns in each processo

PSPOCON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSPOEQU()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSPORFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSPOSV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSPOSVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSPOTF2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSPOTRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSPOTRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSPOTRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSPTSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PSPTTRF()

number of columns in each processo

PSPTTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PSPTTRSV()

number of columns in each processo

PSRSCL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSSTEBZ()

iblock  (global output) integer array, dimension (n)
at each row/column j where e(j) is zero or small, th
matrix.  on exit iblock(i) specifies which block (from 1

PSSTEIN()

process. psstein decides on the allocation of work among the
processes and then calls sstein2 (modified lapack routine) on each
expected orthogonalization may not be done.

PSSYEV()

=====
a description vector is associated with each 2d block-cyclicly dis
establish the mapping between a matrix entry and its corresponding

PSSYEVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSSYGS2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSSYGST()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSSYGVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSSYNGST()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSSYNTRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSSYTD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSSYTRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSSYTTRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding

PSTRCON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSTRRFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSTRTI2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSTRTRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSTRTRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PSTZRZF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZDBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*max(bwl,bwu)

PZDBTRF()

number of columns in each processo

PZDBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*max(bwl,bwu)

PZDBTRSV()

number of columns in each processo

PZDRSCL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZDTSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PZDTTRF()

number of columns in each processo

PZDTTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PZDTTRSV()

number of columns in each processo

PZGBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= (bwl+bwu)+1

PZGBTRF()

number of columns in each processo

PZGBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= (bwl+bwu)+1

PZGEBD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGEBRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGECON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGEEQU()

the column scale factors, chosen to try to make the largest entry in
each row and column of the distributed matrix b with element

PZGEHD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGEHRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGELQ2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGELQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGELS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGEQL2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGEQLF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGEQPF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGEQR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGEQRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGERFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGERQ2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGERQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGESV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGESVD()

=====
each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGESVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGETF2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGETRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGETRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGETRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGGQRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZGGRQF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZHEEV()

=====
a description vector is associated with each 2d block-cyclicly dis
establish the mapping between a matrix entry and its corresponding

PZHEEVD()

query is assumed; the routine calculates the size for all
work arrays. each of these values is returned in the firs
is issued by pxerbla.

PZHEEVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZHEGS2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZHEGST()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZHEGVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZHENGST()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZHENTRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZHETD2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZHETRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZHETTRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding

PZLABRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLACGV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLACON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLACONSB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLACP2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLACP3()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLACPY()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLAEVSWP()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLAHQR()

the main loop begins here. i is the loop index and decreases from
ihi to ilo in steps of our schur block size (<=2*iblk). each
and columns l to i.   eigenvalues i+1 to ihi have already

PZLAHRD()

each h(i) has the for
h(i) = i - tau * v * v'

PZLANGE()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLAPIV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLAPV2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLAQGE()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLAQSY()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLARFB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLARFG()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLARFT()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLARZB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLARZT()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLASCL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLASE2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLASET()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLASMSUB()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLASSQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLASWP()

the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1).  one
interchange is initiated for each of rows or columns k1 trough k2 o
already been broadcast along the process row or column.

PZLATRA()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLATRD()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLATRZ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLATTRS()

compute the 1-norm of each column, not including the diagonal

PZLAUU2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLAUUM()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZLAWIL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZMAX1()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZPBSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*bw

PZPBTRF()

number of columns in each processo

PZPBTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2*bw

PZPBTRSV()

number of columns in each processo

PZPOCON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZPOEQU()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZPORFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZPOSV()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZPOSVX()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZPOTF2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZPOTRF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZPOTRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZPOTRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZPTSV()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PZPTTRF()

number of columns in each processo

PZPTTRS()

if the matrix spans more than one processor, the following
restriction on nb, the size of each block on each processor
nb >= 2

PZPTTRSV()

number of columns in each processo

PZSTEIN()

process. pzstein decides on the allocation of work among the
processes and then calls dstein2 (modified lapack routine) on each
expected orthogonalization may not be done.

PZTRCON()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZTREVC()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZTRRFS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZTRTI2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZTRTRI()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZTRTRS()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZTZRZF()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNG2L()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNG2R()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNGL2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNGLQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNGQL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNGQR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNGR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNGRQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNM2L()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNM2R()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNMBR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNMHR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNML2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNMLQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNMQL()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNMQR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNMR2()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNMR3()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNMRQ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNMRZ()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

PZUNMTR()

each global data object is described by an associated descriptio
the mapping between an object element and its corresponding process

SSTEQR2()

determine where the matrix splits and choose ql or qr iteration
for each block, according to whether top or bottom diagona

ZLAHQR2()

the main loop begins here. i is the loop index and decreases from
ihi to ilo in steps of 1 or 2. each iteration of the loop work
eigenvalues i+1 to ihi have already converged. either l = ilo, or

ease

PCDBTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor

PCDTTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor

PCPBTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor
{f_i}^c =  {h_i}{{b'}_i}^c

PCPTTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor
{f_i}^c =  {h_i}{{b'}_i}^c

PDDBTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor

PDDTTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor

PDPBTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor
{f_i}^t =  {h_i}{{b'}_i}^t

PDPTTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor
{f_i}^t =  {h_i}{{b'}_i}^t

PSDBTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor

PSDTTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor

PSPBTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor
{f_i}^t =  {h_i}{{b'}_i}^t

PSPTTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor
{f_i}^t =  {h_i}{{b'}_i}^t

PZDBTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor

PZDTTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor

PZPBTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor
{f_i}^c =  {h_i}{{b'}_i}^c

PZPTTRF()

calculate off-diagonal block(s) of reduced system.
note: for ease of use in solution of reduced system, stor
{f_i}^c =  {h_i}{{b'}_i}^c

easiest

PCHETTRD()

the value of a is confusing.  it is easiest to state th
so we will start there.

PDSYTTRD()

the value of a is confusing.  it is easiest to state th
so we will start there.

PSSYTTRD()

the value of a is confusing.  it is easiest to state th
so we will start there.

PZHETTRD()

the value of a is confusing.  it is easiest to state th
so we will start there.

easily

DLASORTE()

dlasorte sorts eigenpairs so that real eigenpairs are together and
complex are together.  this way one can employ 2x2 shifts easily
this routine does no parallel work.

SLASORTE()

slasorte sorts eigenpairs so that real eigenpairs are together and
complex are together.  this way one can employ 2x2 shifts easily
this routine does no parallel work.

easy

PCDBTRF()

convert descriptor into standard form for easy access t

PCDBTRSV()

convert descriptor into standard form for easy access t

PCDTTRF()

convert descriptor into standard form for easy access t

PCDTTRSV()

convert descriptor into standard form for easy access t

PCGBTRF()

convert descriptor into standard form for easy access t

PCPBTRF()

convert descriptor into standard form for easy access t

PCPBTRSV()

convert descriptor into standard form for easy access t

PCPTTRF()

convert descriptor into standard form for easy access t

PCPTTRSV()

convert descriptor into standard form for easy access t

PDDBTRF()

convert descriptor into standard form for easy access t

PDDBTRSV()

convert descriptor into standard form for easy access t

PDDTTRF()

convert descriptor into standard form for easy access t

PDDTTRSV()

convert descriptor into standard form for easy access t

PDGBTRF()

convert descriptor into standard form for easy access t

PDPBTRF()

convert descriptor into standard form for easy access t

PDPBTRSV()

convert descriptor into standard form for easy access t

PDPTTRF()

convert descriptor into standard form for easy access t

PDPTTRSV()

convert descriptor into standard form for easy access t

PSDBTRF()

convert descriptor into standard form for easy access t

PSDBTRSV()

convert descriptor into standard form for easy access t

PSDTTRF()

convert descriptor into standard form for easy access t

PSDTTRSV()

convert descriptor into standard form for easy access t

PSGBTRF()

convert descriptor into standard form for easy access t

PSPBTRF()

convert descriptor into standard form for easy access t

PSPBTRSV()

convert descriptor into standard form for easy access t

PSPTTRF()

convert descriptor into standard form for easy access t

PSPTTRSV()

convert descriptor into standard form for easy access t

PZDBTRF()

convert descriptor into standard form for easy access t

PZDBTRSV()

convert descriptor into standard form for easy access t

PZDTTRF()

convert descriptor into standard form for easy access t

PZDTTRSV()

convert descriptor into standard form for easy access t

PZGBTRF()

convert descriptor into standard form for easy access t

PZPBTRF()

convert descriptor into standard form for easy access t

PZPBTRSV()

convert descriptor into standard form for easy access t

PZPTTRF()

convert descriptor into standard form for easy access t

PZPTTRSV()

convert descriptor into standard form for easy access t

edu

PCHEEVX()

where norm(t) is the 1-norm of the tridiagonal matrix
obtained by reducing a to tridiagonal form
eigenvalues will be computed most accurately when abstol is

PCHEGVX()

where norm(t) is the 1-norm of the tridiagonal matrix
obtained by reducing a to tridiagonal form
eigenvalues will be computed most accurately when abstol is

PDSYEVX()

where norm(t) is the 1-norm of the tridiagonal matrix
obtained by reducing a to tridiagonal form
eigenvalues will be computed most accurately when abstol is

PDSYGVX()

where norm(t) is the 1-norm of the tridiagonal matrix
obtained by reducing a to tridiagonal form
eigenvalues will be computed most accurately when abstol is

PSSYEVX()

where norm(t) is the 1-norm of the tridiagonal matrix
obtained by reducing a to tridiagonal form
eigenvalues will be computed most accurately when abstol is

PSSYGVX()

where norm(t) is the 1-norm of the tridiagonal matrix
obtained by reducing a to tridiagonal form
eigenvalues will be computed most accurately when abstol is

PZHEEVX()

where norm(t) is the 1-norm of the tridiagonal matrix
obtained by reducing a to tridiagonal form
eigenvalues will be computed most accurately when abstol is

PZHEGVX()

where norm(t) is the 1-norm of the tridiagonal matrix
obtained by reducing a to tridiagonal form
eigenvalues will be computed most accurately when abstol is

effect

CLAHQR2()

determine the effect of starting the double-shift q
negligible.

PCGBTRF()

only the eliminations of unknowns > ln-bw have an effect o

PCLACONSB()

pclaconsb looks for two consecutive small subdiagonal elements by
seeing the effect of starting a double shift qr iteratio
subdiagonal negligible.

PDGBTRF()

only the eliminations of unknowns > ln-bw have an effect o

PDLACONSB()

pdlaconsb looks for two consecutive small subdiagonal elements by
seeing the effect of starting a double shift qr iteratio
subdiagonal negligible.

PDSTEBZ()

these eigenvalues are flagged by a negative block
number.  the effect is that the eigenvalues may no
tolerances. this is generally caused by arithmetic

PSGBTRF()

only the eliminations of unknowns > ln-bw have an effect o

PSLACONSB()

pslaconsb looks for two consecutive small subdiagonal elements by
seeing the effect of starting a double shift qr iteratio
subdiagonal negligible.

PSSTEBZ()

these eigenvalues are flagged by a negative block
number.  the effect is that the eigenvalues may no
tolerances. this is generally caused by arithmetic

PZGBTRF()

only the eliminations of unknowns > ln-bw have an effect o

PZLACONSB()

pzlaconsb looks for two consecutive small subdiagonal elements by
seeing the effect of starting a double shift qr iteratio
subdiagonal negligible.

ZLAHQR2()

determine the effect of starting the double-shift q
negligible.

efficiency

PCHEGVX()

on return, rwork(1) contains the amount of workspace
required for optimal efficiency
required to compute eigenvalues efficiently

PCHETTRD()

work ( invt ), or v^t, is stored as a tall skinny
array ( nq x anb-1 ) for efficiency.  since only the lowe
tril(a) * v + v^t * tril(a,-1).  this is performed as

PDSYTTRD()

work ( invt ), or v^t, is stored as a tall skinny
array ( nq x anb-1 ) for efficiency.  since only the lowe
tril(a) * v + v^t * tril(a,-1).  this is performed as

PSSYTTRD()

work ( invt ), or v^t, is stored as a tall skinny
array ( nq x anb-1 ) for efficiency.  since only the lowe
tril(a) * v + v^t * tril(a,-1).  this is performed as

PZHEGVX()

on return, rwork(1) contains the amount of workspace
required for optimal efficiency
required to compute eigenvalues efficiently

PZHETTRD()

work ( invt ), or v^t, is stored as a tall skinny
array ( nq x anb-1 ) for efficiency.  since only the lowe
tril(a) * v + v^t * tril(a,-1).  this is performed as

efficient

PCHEEVX()

on return, work(1) contains the optimal amount of
workspace required for efficient execution
required to compute eigenvalues efficiently

PCLAHQR()

communication can be broken into several parts for
efficient parallelism
loop over all the bulges, just doing the work

PDSYEVX()

on return, work(1) contains the optimal amount of
workspace required for efficient execution
required to compute eigenvalues efficiently

PSSYEVX()

on return, work(1) contains the optimal amount of
workspace required for efficient execution
required to compute eigenvalues efficiently

PZHEEVX()

on return, work(1) contains the optimal amount of
workspace required for efficient execution
required to compute eigenvalues efficiently

PZLAHQR()

communication can be broken into several parts for
efficient parallelism
loop over all the bulges, just doing the work

efficiently

PCHEEVX()

if jobz='n' rwork(1) = optimal amount of workspace
required to compute eigenvalues efficiently
required to compute eigenvalues and eigenvectors

PCHEGVX()

if jobz='n' rwork(1) = optimal amount of workspace
required to compute eigenvalues efficiently
required to compute eigenvalues and eigenvectors

PDSYEVX()

if jobz='n' work(1) = optimal amount of workspace
required to compute eigenvalues efficiently
required to compute eigenvalues and eigenvectors

PDSYGVX()

if jobz='n' work(1) = optimal amount of workspace
required to compute eigenvalues efficiently
required to compute eigenvalues and eigenvectors

PSSYEVX()

if jobz='n' work(1) = optimal amount of workspace
required to compute eigenvalues efficiently
required to compute eigenvalues and eigenvectors

PSSYGVX()

if jobz='n' work(1) = optimal amount of workspace
required to compute eigenvalues efficiently
required to compute eigenvalues and eigenvectors

PZHEEVX()

if jobz='n' rwork(1) = optimal amount of workspace
required to compute eigenvalues efficiently
required to compute eigenvalues and eigenvectors

PZHEGVX()

if jobz='n' rwork(1) = optimal amount of workspace
required to compute eigenvalues efficiently
required to compute eigenvalues and eigenvectors

effort

CLAMSH()

see how consecutive small subdiagonal elements are modified by
subsequent shifts in an effort to maximize the number of bulge
clamsh should only be called when there are multiple shifts/bulges

DLAMSH ()

see how consecutive small subdiagonal elements are modified by
subsequent shifts in an effort to maximize the number of bulge
dlamsh should only be called when there are multiple shifts/bulges

SLAMSH ()

see how consecutive small subdiagonal elements are modified by
subsequent shifts in an effort to maximize the number of bulge
slamsh should only be called when there are multiple shifts/bulges

ZLAMSH()

see how consecutive small subdiagonal elements are modified by
subsequent shifts in an effort to maximize the number of bulge
zlamsh should only be called when there are multiple shifts/bulges

eigen

PCLAEVSWP()

pclaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PDLAEVSWP()

pdlaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PJLAENV()

pjlaenv is called from the scalapack symmetric and hermitian
tailored eigen-routines to choos
for a description of the parameters.

PSLAEVSWP()

pslaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PZLAEVSWP()

pzlaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

eigenpairs

DLASORTE()

dlasorte sorts eigenpairs so that real eigenpairs are together an
since every 2nd subdiagonal is guaranteed to be zero.

PDLAHQR()

sort the eigenpairs so that they are in twos for doubl

PSLAHQR()

sort the eigenpairs so that they are in twos for doubl

SLASORTE()

slasorte sorts eigenpairs so that real eigenpairs are together an
since every 2nd subdiagonal is guaranteed to be zero.

eigenproblem

PCHEGS2()

pchegs2 reduces a complex hermitian-definite generalized eigenproblem

PCHEGST()

pchegst reduces a complex hermitian-definite generalized eigenproblem

PCHEGVX()

the eigenvectors
of a complex generalized hermitian-definite eigenproblem, of the for
sub( b )*sub( a )*x=(lambda)*x.

PCHENGST()

pchengst reduces a complex hermitian-definite generalized
eigenproblem to standard form
pchengst performs the same function as pchegst, but is based on

PDSYGS2()

pdsygs2 reduces a real symmetric-definite generalized eigenproblem

PDSYGST()

pdsygst reduces a real symmetric-definite generalized eigenproblem

PDSYGVX()

the eigenvectors
of a real generalized sy-definite eigenproblem, of the for
sub( b )*sub( a )*x=(lambda)*x.

PDSYNGST()

pdsyngst reduces a complex hermitian-definite generalized
eigenproblem to standard form
pdsyngst performs the same function as pdhegst, but is based on

PSSYGS2()

pssygs2 reduces a real symmetric-definite generalized eigenproblem

PSSYGST()

pssygst reduces a real symmetric-definite generalized eigenproblem

PSSYGVX()

the eigenvectors
of a real generalized sy-definite eigenproblem, of the for
sub( b )*sub( a )*x=(lambda)*x.

PSSYNGST()

pssyngst reduces a complex hermitian-definite generalized
eigenproblem to standard form
pssyngst performs the same function as pshegst, but is based on

PZHEGS2()

pzhegs2 reduces a complex hermitian-definite generalized eigenproblem

PZHEGST()

pzhegst reduces a complex hermitian-definite generalized eigenproblem

PZHEGVX()

the eigenvectors
of a complex generalized hermitian-definite eigenproblem, of the for
sub( b )*sub( a )*x=(lambda)*x.

PZHENGST()

pzhengst reduces a complex hermitian-definite generalized
eigenproblem to standard form
pzhengst performs the same function as pzhegst, but is based on

eigensystem

CSTEQR2()

if remaining matrix is 2-by-2, use slae2 or slaev2
to compute its eigensystem

DSTEQR2()

if remaining matrix is 2-by-2, use dlae2 or slaev2
to compute its eigensystem

PDLAED1()

pdlaed1 computes the updated eigensystem of a diagona
in parallel.

PSLAED1()

pslaed1 computes the updated eigensystem of a diagona
in parallel.

SSTEQR2()

if remaining matrix is 2-by-2, use slae2 or slaev2
to compute its eigensystem

ZSTEQR2()

if remaining matrix is 2-by-2, use dlae2 or dlaev2
to compute its eigensystem

eigenvalue

CSTEQR2()

eigenvalue found

DSTEIN2()

loop through eigenvalues of block nblk

DSTEQR2()

compute the eigenvalues and eigenvectors of the tridiagona

PCHEEV()

pcheev computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.

PCHEEVD()

pcheevd computes all the eigenvalues and eigenvectors of a hermitia

PCHEEVX()

pcheevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PCHEGVX()

pchegvx computes all the eigenvalues, and optionally
of a complex generalized hermitian-definite eigenproblem, of the form

PCSTEIN()

in parallel, using inverse iteration. the eigenvectors found
correspond to user specified eigenvalues. pcstein does no
of orthogonalization is controlled by the input parameter lwork.

PCTREVC()

the right eigenvector x and the left eigenvector y of t corresponding
to an eigenvalue w are defined by
t*x = w*x,     y'*t = w*y'

PDLAED0()

pdlaed0 computes all eigenvalues and corresponding eigenvectors of 

PDLAED1()

the eigenvectors of the original matrix are stored in q, and the
eigenvalues are in d.  the algorithm consists of three stages
the first stage consists of deflating the size of the problem

PDLAED2()

pdlaed2 sorts the two sets of eigenvalues together into a singl
there are two ways in which deflation can occur:  when two or more

PDLAED3()

k      (output) integer
the number of non-deflated eigenvalues, and the order of th

PDSTEBZ()

pdstebz computes the eigenvalues of a symmetric tridiagonal matrix i
the interval [vl, vu], or the eigenvalues indexed il through iu. a

PDSTEDC()

=======
pdstedc computes all eigenvalues and eigenvectors of 
conquer algorithm.

PDSTEIN()

in parallel, using inverse iteration. the eigenvectors found
correspond to user specified eigenvalues. pdstein does no
of orthogonalization is controlled by the input parameter lwork.

PDSYEV()

pdsyev computes all eigenvalues and, optionally, eigenvector
of scalapack routines.

PDSYEVD()

pdsyevd computes  all the eigenvalues and eigenvector
of scalapack routines.

PDSYEVX()

pdsyevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PDSYGVX()

pdsygvx computes all the eigenvalues, and optionally
of a real generalized sy-definite eigenproblem, of the form

PSLAED0()

pslaed0 computes all eigenvalues and corresponding eigenvectors of 

PSLAED1()

the eigenvectors of the original matrix are stored in q, and the
eigenvalues are in d.  the algorithm consists of three stages
the first stage consists of deflating the size of the problem

PSLAED2()

pslaed2 sorts the two sets of eigenvalues together into a singl
there are two ways in which deflation can occur:  when two or more

PSLAED3()

k      (output) integer
the number of non-deflated eigenvalues, and the order of th

PSSTEBZ()

psstebz computes the eigenvalues of a symmetric tridiagonal matrix i
the interval [vl, vu], or the eigenvalues indexed il through iu. a

PSSTEDC()

=======
psstedc computes all eigenvalues and eigenvectors of 
conquer algorithm.

PSSTEIN()

in parallel, using inverse iteration. the eigenvectors found
correspond to user specified eigenvalues. psstein does no
of orthogonalization is controlled by the input parameter lwork.

PSSYEV()

pssyev computes all eigenvalues and, optionally, eigenvector
of scalapack routines.

PSSYEVD()

pssyevd computes  all the eigenvalues and eigenvector
of scalapack routines.

PSSYEVX()

pssyevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PSSYGVX()

pssygvx computes all the eigenvalues, and optionally
of a real generalized sy-definite eigenproblem, of the form

PZHEEV()

pzheev computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.

PZHEEVD()

pzheevd computes all the eigenvalues and eigenvectors of a hermitia

PZHEEVX()

pzheevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PZHEGVX()

pzhegvx computes all the eigenvalues, and optionally
of a complex generalized hermitian-definite eigenproblem, of the form

PZSTEIN()

in parallel, using inverse iteration. the eigenvectors found
correspond to user specified eigenvalues. pzstein does no
of orthogonalization is controlled by the input parameter lwork.

PZTREVC()

the right eigenvector x and the left eigenvector y of t corresponding
to an eigenvalue w are defined by
t*x = w*x,     y'*t = w*y'

SSTEIN2()

loop through eigenvalues of block nblk

SSTEQR2()

compute the eigenvalues and eigenvectors of the tridiagona

ZSTEQR2()

eigenvalue found

eigenvalues

CLAHQR2()

i1 and i2 are the indices of the first row and last column of h
to which transformations must be applied. if eigenvalues only ar

CLANV2()

rt2     (output) complex
the two eigenvalues
cs      (output) real

DLASORTE()

on exit, the diagonal blocks of s have been rewritten to pair
the eigenvalues.  the resulting matrix is no longe

DSTEIN2()

loop through eigenvalues of block nblk

DSTEQR2()

compute the eigenvalues and eigenvectors of the tridiagona

PCHEEV()

pcheev computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.

PCHEEVD()

pcheevd computes all the eigenvalues and eigenvectors of a hermitia

PCHEEVX()

pcheevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PCHEGST()

scale   (global output) real
amount by which the eigenvalues should be scaled t
at present, scale is always returned as 1.0, it is

PCHEGVX()

pchegvx computes all the eigenvalues, and optionally
of a complex generalized hermitian-definite eigenproblem, of the form

PCHENGST()

scale   (global output) real
amount by which the eigenvalues should be scaled t
at present, scale is always returned as 1.0, it is

PCLAEVSWP()

where they are computed, to a scalapack standard block cyclic
array, sorted so that the corresponding eigenvalues are sorted
notes

PCLAHQR()

i1 and i2 are the indices of the first row and last column of h
to which transformations must be applied. if eigenvalues only ar

PCSTEIN()

in parallel, using inverse iteration. the eigenvectors found
correspond to user specified eigenvalues. pcstein does no
of orthogonalization is controlled by the input parameter lwork.

PCTREVC()

of vl, in the same order as their
eigenvalues

PDLAEBZ()

pdlaebz contains the iteration loop which computes the eigenvalues
j = 1,...,minp. it uses and computes the function n(w), which is

PDLAED0()

pdlaed0 computes all eigenvalues and corresponding eigenvectors of 

PDLAED1()

the eigenvectors of the original matrix are stored in q, and the
eigenvalues are in d.  the algorithm consists of three stages
the first stage consists of deflating the size of the problem

PDLAED2()

pdlaed2 sorts the two sets of eigenvalues together into a singl
there are two ways in which deflation can occur:  when two or more

PDLAED3()

k      (output) integer
the number of non-deflated eigenvalues, and the order of th

PDLAEVSWP()

where they are computed, to a scalapack standard block cyclic
array, sorted so that the corresponding eigenvalues are sorted
notes

PDLAHQR()

i1 and i2 are the indices of the first row and last column of h
to which transformations must be applied. if eigenvalues only ar

PDLAPDCT()

pdlapdct counts the number of negative eigenvalues of (t - sigma i)
the innermost loop to avoid overflow and determine the sign of a

PDSTEBZ()

pdstebz computes the eigenvalues of a symmetric tridiagonal matrix i
the interval [vl, vu], or the eigenvalues indexed il through iu. a

PDSTEDC()

=======
pdstedc computes all eigenvalues and eigenvectors of 
conquer algorithm.

PDSTEIN()

in parallel, using inverse iteration. the eigenvectors found
correspond to user specified eigenvalues. pdstein does no
of orthogonalization is controlled by the input parameter lwork.

PDSYEV()

pdsyev computes all eigenvalues and, optionally, eigenvector
of scalapack routines.

PDSYEVD()

pdsyevd computes  all the eigenvalues and eigenvector
of scalapack routines.

PDSYEVX()

pdsyevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PDSYGST()

scale   (global output) double precision
amount by which the eigenvalues should be scaled t
at present, scale is always returned as 1.0, it is

PDSYGVX()

pdsygvx computes all the eigenvalues, and optionally
of a real generalized sy-definite eigenproblem, of the form

PDSYNGST()

scale   (global output) double precision
amount by which the eigenvalues should be scaled t
at present, scale is always returned as 1.0, it is

PSLAEBZ()

pslaebz contains the iteration loop which computes the eigenvalues
j = 1,...,minp. it uses and computes the function n(w), which is

PSLAED0()

pslaed0 computes all eigenvalues and corresponding eigenvectors of 

PSLAED1()

the eigenvectors of the original matrix are stored in q, and the
eigenvalues are in d.  the algorithm consists of three stages
the first stage consists of deflating the size of the problem

PSLAED2()

pslaed2 sorts the two sets of eigenvalues together into a singl
there are two ways in which deflation can occur:  when two or more

PSLAED3()

k      (output) integer
the number of non-deflated eigenvalues, and the order of th

PSLAEVSWP()

where they are computed, to a scalapack standard block cyclic
array, sorted so that the corresponding eigenvalues are sorted
notes

PSLAHQR()

i1 and i2 are the indices of the first row and last column of h
to which transformations must be applied. if eigenvalues only ar

PSLAPDCT()

pslapdct counts the number of negative eigenvalues of (t - sigma i)
the innermost loop to avoid overflow and determine the sign of a

PSSTEBZ()

psstebz computes the eigenvalues of a symmetric tridiagonal matrix i
the interval [vl, vu], or the eigenvalues indexed il through iu. a

PSSTEDC()

=======
psstedc computes all eigenvalues and eigenvectors of 
conquer algorithm.

PSSTEIN()

in parallel, using inverse iteration. the eigenvectors found
correspond to user specified eigenvalues. psstein does no
of orthogonalization is controlled by the input parameter lwork.

PSSYEV()

pssyev computes all eigenvalues and, optionally, eigenvector
of scalapack routines.

PSSYEVD()

pssyevd computes  all the eigenvalues and eigenvector
of scalapack routines.

PSSYEVX()

pssyevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PSSYGST()

scale   (global output) real
amount by which the eigenvalues should be scaled t
at present, scale is always returned as 1.0, it is

PSSYGVX()

pssygvx computes all the eigenvalues, and optionally
of a real generalized sy-definite eigenproblem, of the form

PSSYNGST()

scale   (global output) real
amount by which the eigenvalues should be scaled t
at present, scale is always returned as 1.0, it is

PZHEEV()

pzheev computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.

PZHEEVD()

pzheevd computes all the eigenvalues and eigenvectors of a hermitia

PZHEEVX()

pzheevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PZHEGST()

scale   (global output) double precision
amount by which the eigenvalues should be scaled t
at present, scale is always returned as 1.0, it is

PZHEGVX()

pzhegvx computes all the eigenvalues, and optionally
of a complex generalized hermitian-definite eigenproblem, of the form

PZHENGST()

scale   (global output) double precision
amount by which the eigenvalues should be scaled t
at present, scale is always returned as 1.0, it is

PZLAEVSWP()

where they are computed, to a scalapack standard block cyclic
array, sorted so that the corresponding eigenvalues are sorted
notes

PZLAHQR()

i1 and i2 are the indices of the first row and last column of h
to which transformations must be applied. if eigenvalues only ar

PZSTEIN()

in parallel, using inverse iteration. the eigenvectors found
correspond to user specified eigenvalues. pzstein does no
of orthogonalization is controlled by the input parameter lwork.

PZTREVC()

of vl, in the same order as their
eigenvalues

SLASORTE()

on exit, the diagonal blocks of s have been rewritten to pair
the eigenvalues.  the resulting matrix is no longe

SSTEIN2()

loop through eigenvalues of block nblk

SSTEQR2()

compute the eigenvalues and eigenvectors of the tridiagona

ZLAHQR2()

i1 and i2 are the indices of the first row and last column of h
to which transformations must be applied. if eigenvalues only ar

ZLANV2()

rt2     (output) complex*16
the two eigenvalues
cs      (output) double precision

eigenvector

DSTEIN2()

compute eigenvectors of matrix blocks

PCHEEVX()

pcheevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PCHEGVX()

pchegvx computes all the eigenvalues, and optionally,
the eigenvector
sub( a )*x=(lambda)*sub( b )*x,  sub( a )*sub( b )x=(lambda)*x,  or

PCLAEVSWP()

pclaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PCSTEIN()

pcstein computes the eigenvectors of a symmetric tridiagonal matri
correspond to user specified eigenvalues. pcstein does not

PCTREVC()

pctrevc computes some or all of the right and/or left eigenvectors o

PDLAED2()

q      (input/output) double precision array, dimension (ldq, n)
on entry, q contains the eigenvectors of two submatrices i
and (n1+1, n1+1), (n,n).

PDLAED3()

q      (input/output) double precision array, dimension (ldq, n)
on entry, q contains the eigenvectors of two submatrices i
and (n1+1, n1+1), (n,n).

PDLAEVSWP()

pdlaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PDSTEIN()

pdstein computes the eigenvectors of a symmetric tridiagonal matri
correspond to user specified eigenvalues. pdstein does not

PDSYEVX()

pdsyevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PDSYGVX()

pdsygvx computes all the eigenvalues, and optionally,
the eigenvector
sub( a )*x=(lambda)*sub( b )*x,  sub( a )*sub( b )x=(lambda)*x,  or

PSLAED2()

q      (input/output) real array, dimension (ldq, n)
on entry, q contains the eigenvectors of two submatrices i
and (n1+1, n1+1), (n,n).

PSLAED3()

q      (input/output) real array, dimension (ldq, n)
on entry, q contains the eigenvectors of two submatrices i
and (n1+1, n1+1), (n,n).

PSLAEVSWP()

pslaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PSSTEIN()

psstein computes the eigenvectors of a symmetric tridiagonal matri
correspond to user specified eigenvalues. psstein does not

PSSYEVX()

pssyevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PSSYGVX()

pssygvx computes all the eigenvalues, and optionally,
the eigenvector
sub( a )*x=(lambda)*sub( b )*x,  sub( a )*sub( b )x=(lambda)*x,  or

PZHEEVX()

pzheevx computes selected eigenvalues and, optionally, eigenvector
of scalapack routines.  eigenvalues/vectors can be selected by

PZHEGVX()

pzhegvx computes all the eigenvalues, and optionally,
the eigenvector
sub( a )*x=(lambda)*sub( b )*x,  sub( a )*sub( b )x=(lambda)*x,  or

PZLAEVSWP()

pzlaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PZSTEIN()

pzstein computes the eigenvectors of a symmetric tridiagonal matri
correspond to user specified eigenvalues. pzstein does not

PZTREVC()

pztrevc computes some or all of the right and/or left eigenvectors o

SSTEIN2()

compute eigenvectors of matrix blocks

eigenvectors

CSTEQR2()

if eigenvectors are desired, then save rotations

DSTEIN2()

compute eigenvectors of matrix blocks

DSTEQR2()

compute the eigenvalues and eigenvectors of the tridiagona

PCHEEV()

pcheev computes selected eigenvalues and, optionally, eigenvectors
of scalapack routines.

PCHEEVD()

pcheevd computes all the eigenvalues and eigenvectors of a hermitia

PCHEEVX()

pcheevx computes selected eigenvalues and, optionally, eigenvectors
of scalapack routines.  eigenvalues/vectors can be selected by

PCHEGVX()

pchegvx computes all the eigenvalues, and optionally,
the eigenvectors
sub( a )*x=(lambda)*sub( b )*x,  sub( a )*sub( b )x=(lambda)*x,  or

PCLAEVSWP()

pclaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PCSTEIN()

pcstein computes the eigenvectors of a symmetric tridiagonal matri
correspond to user specified eigenvalues. pcstein does not

PCTREVC()

pctrevc computes some or all of the right and/or left eigenvectors o

PDLAED0()

pdlaed0 computes all eigenvalues and corresponding eigenvectors of 

PDLAED1()

the eigenvectors of the original matrix are stored in q, and th

PDLAED2()

q      (input/output) double precision array, dimension (ldq, n)
on entry, q contains the eigenvectors of two submatrices i
and (n1+1, n1+1), (n,n).

PDLAED3()

q      (input/output) double precision array, dimension (ldq, n)
on entry, q contains the eigenvectors of two submatrices i
and (n1+1, n1+1), (n,n).

PDLAEVSWP()

pdlaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PDSTEBZ()

set to the underflow threshold dlamch('u'), not zero.
note : if eigenvectors are desired later by inverse iteratio

PDSTEDC()

=======
pdstedc computes all eigenvalues and eigenvectors of 
conquer algorithm.

PDSTEIN()

pdstein computes the eigenvectors of a symmetric tridiagonal matri
correspond to user specified eigenvalues. pdstein does not

PDSYEV()

pdsyev computes all eigenvalues and, optionally, eigenvectors
of scalapack routines.

PDSYEVD()

pdsyevd computes  all the eigenvalues and eigenvectors
of scalapack routines.

PDSYEVX()

pdsyevx computes selected eigenvalues and, optionally, eigenvectors
of scalapack routines.  eigenvalues/vectors can be selected by

PDSYGVX()

pdsygvx computes all the eigenvalues, and optionally,
the eigenvectors
sub( a )*x=(lambda)*sub( b )*x,  sub( a )*sub( b )x=(lambda)*x,  or

PSLAED0()

pslaed0 computes all eigenvalues and corresponding eigenvectors of 

PSLAED1()

the eigenvectors of the original matrix are stored in q, and th

PSLAED2()

q      (input/output) real array, dimension (ldq, n)
on entry, q contains the eigenvectors of two submatrices i
and (n1+1, n1+1), (n,n).

PSLAED3()

q      (input/output) real array, dimension (ldq, n)
on entry, q contains the eigenvectors of two submatrices i
and (n1+1, n1+1), (n,n).

PSLAEVSWP()

pslaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PSSTEBZ()

set to the underflow threshold slamch('u'), not zero.
note : if eigenvectors are desired later by inverse iteratio

PSSTEDC()

=======
psstedc computes all eigenvalues and eigenvectors of 
conquer algorithm.

PSSTEIN()

psstein computes the eigenvectors of a symmetric tridiagonal matri
correspond to user specified eigenvalues. psstein does not

PSSYEV()

pssyev computes all eigenvalues and, optionally, eigenvectors
of scalapack routines.

PSSYEVD()

pssyevd computes  all the eigenvalues and eigenvectors
of scalapack routines.

PSSYEVX()

pssyevx computes selected eigenvalues and, optionally, eigenvectors
of scalapack routines.  eigenvalues/vectors can be selected by

PSSYGVX()

pssygvx computes all the eigenvalues, and optionally,
the eigenvectors
sub( a )*x=(lambda)*sub( b )*x,  sub( a )*sub( b )x=(lambda)*x,  or

PZHEEV()

pzheev computes selected eigenvalues and, optionally, eigenvectors
of scalapack routines.

PZHEEVD()

pzheevd computes all the eigenvalues and eigenvectors of a hermitia

PZHEEVX()

pzheevx computes selected eigenvalues and, optionally, eigenvectors
of scalapack routines.  eigenvalues/vectors can be selected by

PZHEGVX()

pzhegvx computes all the eigenvalues, and optionally,
the eigenvectors
sub( a )*x=(lambda)*sub( b )*x,  sub( a )*sub( b )x=(lambda)*x,  or

PZLAEVSWP()

pzlaevswp moves the eigenvectors (potentially unsorted) fro
array, sorted so that the corresponding eigenvalues are sorted.

PZSTEIN()

pzstein computes the eigenvectors of a symmetric tridiagonal matri
correspond to user specified eigenvalues. pzstein does not

PZTREVC()

pztrevc computes some or all of the right and/or left eigenvectors o

SSTEIN2()

compute eigenvectors of matrix blocks

SSTEQR2()

compute the eigenvalues and eigenvectors of the tridiagona

ZSTEQR2()

if eigenvectors are desired, then save rotations

either

CLAHQR2()

with the active submatrix in rows and columns l to i.
eigenvalues i+1 to ihi have already converged. either l = ilo, o

CLAREF()

claref applies one or several householder reflectors of size 3
to one or two matrices (if column is specified) on either thei

DLAREF()

dlaref applies one or several householder reflectors of size 3
to one or two matrices (if column is specified) on either thei

PCDBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PCDBTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PCDTSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PCDTTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PCGBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PCGBTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PCGECON()

pcgecon estimates the reciprocal of the condition number of a general
distributed complex matrix a(ia:ia+n-1,ja:ja+n-1), in either th
pcgetrf.

PCHENTRD()

pchentrd is a prototype version of pchetrd which uses tailored
codes (either the serial, chetrd, or the parallel code, pchettrd

PCLAHQR()

and columns l to i.   eigenvalues i+1 to ihi have already
converged. either l = ilo or the global a(l,l-1) is negligibl

PCLAPIV()

pclapiv applies either p (permutation matrix indicated by ipiv
sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column

PCLAPV2()

pclapv2 applies either p (permutation matrix indicated by ipiv
a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting.  the

PCPBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PCPBTRS()

matrix with bandwidth bw.
depending on the value of uplo, a stores either u or l in the equ

PCPTSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PCPTTRS()

matrix.
depending on the value of uplo, a stores either u or l in the equ

PCTRCON()

pctrcon estimates the reciprocal of the condition number of a
triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th

PCTREVC()

if all eigenvectors are requested, the routine may either return th
products q*x and/or q*y, where q is an input unitary

PDDBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PDDBTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PDDTSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PDDTTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PDGBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PDGBTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PDGECON()

pdgecon estimates the reciprocal of the condition number of a general
distributed real matrix a(ia:ia+n-1,ja:ja+n-1), in either the 1-nor

PDLAHQR()

and columns l to i.   eigenvalues i+1 to ihi have already
converged. either l = ilo or the global a(l,l-1) is negligibl

PDLAPIV()

pdlapiv applies either p (permutation matrix indicated by ipiv
sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column

PDLAPV2()

pdlapv2 applies either p (permutation matrix indicated by ipiv
a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting.  the

PDPBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PDPBTRS()

matrix with bandwidth bw.
depending on the value of uplo, a stores either u or l in the equ

PDPTSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PDPTTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PDSYNTRD()

pdsyntrd is a prototype version of pdsytrd which uses tailored
codes (either the serial, dsytrd, or the parallel code, pdsyttrd

PDTRCON()

pdtrcon estimates the reciprocal of the condition number of a
triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th

PJLAENV()

name    (global input) character*(*)
the name of the calling subroutine, in either upper case o

PSDBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PSDBTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PSDTSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PSDTTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PSGBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PSGBTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PSGECON()

psgecon estimates the reciprocal of the condition number of a general
distributed real matrix a(ia:ia+n-1,ja:ja+n-1), in either the 1-nor

PSLAHQR()

and columns l to i.   eigenvalues i+1 to ihi have already
converged. either l = ilo or the global a(l,l-1) is negligibl

PSLAPIV()

pslapiv applies either p (permutation matrix indicated by ipiv
sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column

PSLAPV2()

pslapv2 applies either p (permutation matrix indicated by ipiv
a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting.  the

PSPBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PSPBTRS()

matrix with bandwidth bw.
depending on the value of uplo, a stores either u or l in the equ

PSPTSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PSPTTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PSSYNTRD()

pssyntrd is a prototype version of pssytrd which uses tailored
codes (either the serial, ssytrd, or the parallel code, pssyttrd

PSTRCON()

pstrcon estimates the reciprocal of the condition number of a
triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th

PZDBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PZDBTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PZDTSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PZDTTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PZGBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PZGBTRS()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PZGECON()

pzgecon estimates the reciprocal of the condition number of a general
distributed complex matrix a(ia:ia+n-1,ja:ja+n-1), in either th
pzgetrf.

PZHENTRD()

pzhentrd is a prototype version of pzhetrd which uses tailored
codes (either the serial, zhetrd, or the parallel code, pzhettrd

PZLAHQR()

and columns l to i.   eigenvalues i+1 to ihi have already
converged. either l = ilo or the global a(l,l-1) is negligibl

PZLAPIV()

pzlapiv applies either p (permutation matrix indicated by ipiv
sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column

PZLAPV2()

pzlapv2 applies either p (permutation matrix indicated by ipiv
a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting.  the

PZPBSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PZPBTRS()

matrix with bandwidth bw.
depending on the value of uplo, a stores either u or l in the equ

PZPTSV()

the index in the global array a that points to the start of
the matrix to be operated on (which may be either all of 

PZPTTRS()

matrix.
depending on the value of uplo, a stores either u or l in the equ

PZTRCON()

pztrcon estimates the reciprocal of the condition number of a
triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th

PZTREVC()

if all eigenvectors are requested, the routine may either return th
products q*x and/or q*y, where q is an input unitary

SLAREF()

slaref applies one or several householder reflectors of size 3
to one or two matrices (if column is specified) on either thei

ZLAHQR2()

with the active submatrix in rows and columns l to i.
eigenvalues i+1 to ihi have already converged. either l = ilo, o

ZLAREF()

zlaref applies one or several householder reflectors of size 3
to one or two matrices (if column is specified) on either thei

ele

PCGEHD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGEHRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGETRF()

the factorization has the form sub( a ) = p * l * u, where p is a
permutation matrix, l is lower triangular with unit diagonal ele
(upper trapezoidal if m < n). l and u are stored in sub( a ).

PDGEHD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGEHRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGETRF()

the factorization has the form sub( a ) = p * l * u, where p is a
permutation matrix, l is lower triangular with unit diagonal ele
(upper trapezoidal if m < n). l and u are stored in sub( a ).

PSGEHD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGEHRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGETRF()

the factorization has the form sub( a ) = p * l * u, where p is a
permutation matrix, l is lower triangular with unit diagonal ele
(upper trapezoidal if m < n). l and u are stored in sub( a ).

PZGEHD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PZGEHRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PZGETRF()

the factorization has the form sub( a ) = p * l * u, where p is a
permutation matrix, l is lower triangular with unit diagonal ele
(upper trapezoidal if m < n). l and u are stored in sub( a ).

elemen

PCUNM2L()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PCUNM2R()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PCUNMQL()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PCUNMQR()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PDORM2L()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PDORM2R()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PDORMQL()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PDORMQR()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PSORM2L()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PSORM2R()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PSORMQL()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PSORMQR()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PZUNM2L()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PZUNM2R()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PZUNMQL()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PZUNMQR()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

element

CCOMBAMAX1 ()

ccombamax1 finds the element having maximum real part absolut

CLAHQR2()

submatrix of order 1 or 2 splits off at the bottom because a
subdiagonal element has become negligible

CLAREF()

irow1   (local input/output) integer
on entry, the local row element of a

CSTEQR2()

look for small superdiagonal element

CTRMVT()

where x is an n element vector and  t is an n by 

DLAREF()

irow1   (local input/output) integer
on entry, the local row element of a

DSTEQR2()

for each block, according to whether top or bottom diagonal
element is smaller

DTRMVT()

where x is an n element vector and  t is an n by 

PCDBSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCDBTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCDTSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCDTTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGBSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGBTRF()

offset in element

PCGBTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGEBD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGEBRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGECON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGEEQU()

the column scale factors, chosen to try to make the largest entry in
each row and column of the distributed matrix b with element

PCGEHD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGEHRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGELQ2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGELQF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGELS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGEQL2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGEQLF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGEQPF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGEQR2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGEQRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGERFS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGERQ2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGERQF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGESV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGESVD()

where sigma is an m-by-n matrix which is zero except for its
min(m,n) diagonal elements, u is an m-by-m orthogonal matrix, an
are the singular values of a and the columns of u and v are the

PCGESVX()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGETF2()

permutation matrix, l is lower triangular with unit diagonal
elements (lower trapezoidal if m > n), and u is upper triangula

PCGETRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGETRI()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGETRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGGQRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCGGRQF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCHEEV()

and assume that its process grid has dimension p x q.
locr( k ) denotes the number of elements of k that a proces
process column.

PCHEEVX()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCHEGS2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCHEGST()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCHEGVX()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCHENGST()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCHENTRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCHETD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCHETRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCHETTRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its correspondin

PCLABRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLACGV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLACON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLACONSB()

pclaconsb looks for two consecutive small subdiagonal elements b
given by h44, h33, & h43h34 and see if this would make a

PCLACP2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLACP3()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLACPY()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLAEVSWP()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLAHQR()

submatrix of order 1 or 2 splits off at the bottom because a
subdiagonal element has become negligible

PCLAHRD()

n-by-(n-k+1) distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that
elements below the k-th subdiagonal are zero. the reduction i
routine returns the matrices v and t which determine q as a block

PCLANGE()

pclange returns the value of the one norm, or the frobenius norm,
or the infinity norm, or the element of largest absolute value of 

PCLAPIV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLAPV2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLAQGE()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLAQSY()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLARFB()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLARFG()

pclarfg generates a complex elementary reflector h of order n, suc

PCLARFT()

pclarft forms the triangular factor t of a complex block reflector h
of order n, which is defined as a product of k elementary reflectors
if direct = 'f', h = h(1) h(2) . . . h(k) and t is upper triangular;

PCLARZB()

q is a product of k elementary reflectors as returned by pctzrzf
currently, only storev = 'r' and direct = 'b' are supported.

PCLARZT()

pclarzt forms the triangular factor t of a complex block reflector
h of order > n, which is defined as a product of k elementar

PCLASCL()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLASE2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLASET()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLASMSUB()

pclasmsub looks for a small subdiagonal element from the botto

PCLASSQ()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLASWP()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLATRA()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLATRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLATRZ()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLATTRS()

scale the column norms by tscal if the maximum element in cnorm i

PCLAUU2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLAUUM()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCLAWIL()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCMAX1()

pcmax1 computes the global index of the maximum element in absolut
in indx and the value is returned in amax,

PCPBSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPBTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPOCON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPOEQU()

factors, s(i) = 1/sqrt(a(i,i)), chosen so that the scaled distri-
buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones o
of b within a factor n of the smallest possible condition number

PCPORFS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPOSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPOSVX()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPOTF2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPOTRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPOTRI()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPOTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPTSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCPTTRF()

perform the triangular system solve {l_i}{{b'}_i}^c = {b_i}^c
by dividing b_i by diagonal element

PCPTTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCSRSCL()

pcsrscl multiplies an n-element complex distributed vecto
underflow as long as the final sub( x )/a does not overflow or

PCSTEIN()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCTRCON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCTREVC()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCTRRFS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCTRTI2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCTRTRI()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCTRTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCTZRZF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PCUNG2L()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the last n columns of a product of k elementary reflectors of order 
q  =  h(k) . . . h(2) h(1)

PCUNG2R()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the first n columns of a product of k elementary reflectors of orde

PCUNGL2()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as
the first m rows of a product of k elementary reflectors of order 
q  =  h(k)' . . . h(2)' h(1)'

PCUNGLQ()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as
the first m rows of a product of k elementary reflectors of order 
q  =  h(k)' . . . h(2)' h(1)'

PCUNGQL()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the last n columns of a product of k elementary reflectors of order 
q  =  h(k) . . . h(2) h(1)

PCUNGQR()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the first n columns of a product of k elementary reflectors of orde

PCUNGR2()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the
last m rows of a product of k elementary reflectors of order 
q  =  h(1)' h(2)' . . . h(k)'

PCUNGRQ()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the
last m rows of a product of k elementary reflectors of order 
q  =  h(1)' h(2)' . . . h(k)'

PCUNM2L()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PCUNM2R()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PCUNMBR()

bidiagonal form: a(ia:*,ja:*) = q * b * p**h. q and p**h are defined
as products of elementary reflectors h(i) and g(i) respectively
let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is the

PCUNMHR()

nq = m if side = 'l' and nq = n if side = 'r'. q is defined as the
product of ihi-ilo elementary reflectors, as returned by pcgehrd
q = h(ilo) h(ilo+1) . . . h(ihi-1).

PCUNML2()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(k)' . . . h(2)' h(1)'

PCUNMLQ()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(k)' . . . h(2)' h(1)'

PCUNMQL()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PCUNMQR()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PCUNMR2()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(1)' h(2)' . . . h(k)'

PCUNMR3()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(1)' h(2)' . . . h(k)'

PCUNMRQ()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(1)' h(2)' . . . h(k)'

PCUNMRZ()

where q is a complex unitary distributed matrix defined as the
product of k elementary reflector
q = h(1)' h(2)' . . . h(k)'

PCUNMTR()

nq = m if side = 'l' and nq = n if side = 'r'. q is defined as the
product of nq-1 elementary reflectors, as returned by pchetrd
if uplo = 'u', q = h(nq-1) . . . h(2) h(1);

PDDBSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDDBTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDDTSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDDTTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGBSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGBTRF()

offset in element

PDGBTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGEBD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGEBRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGECON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGEEQU()

the column scale factors, chosen to try to make the largest entry in
each row and column of the distributed matrix b with element

PDGEHD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGEHRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGELQ2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGELQF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGELS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGEQL2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGEQLF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGEQPF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGEQR2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGEQRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGERFS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGERQ2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGERQF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGESV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGESVD()

where sigma is an m-by-n matrix which is zero except for its
min(m,n) diagonal elements, u is an m-by-m orthogonal matrix, an
are the singular values of a and the columns of u and v are the

PDGESVX()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGETF2()

permutation matrix, l is lower triangular with unit diagonal
elements (lower trapezoidal if m > n), and u is upper triangula

PDGETRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGETRI()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGETRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGGQRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDGGRQF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLABRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLACON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLACONSB()

pdlaconsb looks for two consecutive small subdiagonal elements b
given by h44, h33, & h43h34 and see if this would make a

PDLACP2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLACP3()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLACPY()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLAED2()

rho    (global input/output) double precision
on entry, the off-diagonal element associated with the rank-
being recombined.

PDLAED3()

rho    (global input/output) double precision
on entry, the off-diagonal element associated with the rank-
being recombined.

PDLAEVSWP()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLAHQR()

submatrix of order 1 or 2 splits off at the bottom because a
subdiagonal element has become negligible

PDLAHRD()

pdlahrd reduces the first nb columns of a real general n-by-(n-k+1)
distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that elements below th
nal similarity transformation q' * a * q. the routine returns the

PDLANGE()

pdlange returns the value of the one norm, or the frobenius norm,
or the infinity norm, or the element of largest absolute value of 

PDLAPIV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLAPV2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLAQGE()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLAQSY()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLARED1D()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLARED2D()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLARFB()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLARFG()

pdlarfg generates a real elementary reflector h of order n, suc

PDLARFT()

pdlarft forms the triangular factor t of a real block reflector h
of order n, which is defined as a product of k elementary reflectors
if direct = 'f', h = h(1) h(2) . . . h(k) and t is upper triangular;

PDLARZB()

q is a product of k elementary reflectors as returned by pdtzrzf
currently, only storev = 'r' and direct = 'b' are supported.

PDLARZT()

pdlarzt forms the triangular factor t of a real block reflector
h of order > n, which is defined as a product of k elementar

PDLASCL()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLASE2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLASET()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLASMSUB()

pdlasmsub looks for a small subdiagonal element from the botto

PDLASSQ()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLASWP()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLATRA()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLATRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLATRZ()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLAUU2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLAUUM()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDLAWIL()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDORG2L()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the last n columns of a product of k elementary reflectors of order 
q  =  h(k) . . . h(2) h(1)

PDORG2R()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the first n columns of a product of k elementary reflectors of orde

PDORGL2()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as
the first m rows of a product of k elementary reflectors of order 
q  =  h(k) . . . h(2) h(1)

PDORGLQ()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as
the first m rows of a product of k elementary reflectors of order 
q  =  h(k) . . . h(2) h(1)

PDORGQL()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the last n columns of a product of k elementary reflectors of order 
q  =  h(k) . . . h(2) h(1)

PDORGQR()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the first n columns of a product of k elementary reflectors of orde

PDORGR2()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the
last m rows of a product of k elementary reflectors of order 
q  =  h(1) h(2) . . . h(k)

PDORGRQ()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the
last m rows of a product of k elementary reflectors of order 
q  =  h(1) h(2) . . . h(k)

PDORM2L()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PDORM2R()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PDORMBR()

bidiagonal form: a(ia:*,ja:*) = q * b * p**t. q and p**t are defined
as products of elementary reflectors h(i) and g(i) respectively
let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is the

PDORMHR()

nq = m if side = 'l' and nq = n if side = 'r'. q is defined as the
product of ihi-ilo elementary reflectors, as returned by pdgehrd
q = h(ilo) h(ilo+1) . . . h(ihi-1).

PDORML2()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PDORMLQ()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PDORMQL()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PDORMQR()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PDORMR2()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PDORMR3()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PDORMRQ()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PDORMRZ()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PDORMTR()

nq = m if side = 'l' and nq = n if side = 'r'. q is defined as the
product of nq-1 elementary reflectors, as returned by pdsytrd
if uplo = 'u', q = h(nq-1) . . . h(2) h(1);

PDPBSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPBTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPOCON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPOEQU()

factors, s(i) = 1/sqrt(a(i,i)), chosen so that the scaled distri-
buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones o
of b within a factor n of the smallest possible condition number

PDPORFS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPOSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPOSVX()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPOTF2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPOTRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPOTRI()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPOTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPTSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDPTTRF()

perform the triangular system solve {l_i}{{b'}_i}^t = {b_i}^t
by dividing b_i by diagonal element

PDPTTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDRSCL()

pdrscl multiplies an n-element real distributed vector sub( x ) b
long as the final result sub( x )/a does not overflow or underflow.

PDSTEDC()

d       (global input/output) double precision array, dimension (n)
on entry, the diagonal elements of the tridiagonal matrix

PDSTEIN()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDSYEV()

and assume that its process grid has dimension p x q.
locr( k ) denotes the number of elements of k that a proces
process column.

PDSYEVD()

on entry, the symmetric matrix a.  if uplo = 'u', only the
upper triangular part of a is used to define the elements o
triangular part of a is used to define the elements of the

PDSYEVX()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDSYGS2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDSYGST()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDSYGVX()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDSYNGST()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDSYNTRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDSYTD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDSYTRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDSYTTRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its correspondin

PDTRCON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDTRRFS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDTRTI2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDTRTRI()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDTRTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDTZRZF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PDZSUM1()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSCSUM1()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSDBSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSDBTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSDTSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSDTTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGBSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGBTRF()

offset in element

PSGBTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGEBD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGEBRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGECON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGEEQU()

the column scale factors, chosen to try to make the largest entry in
each row and column of the distributed matrix b with element

PSGEHD2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGEHRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGELQ2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGELQF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGELS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGEQL2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGEQLF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGEQPF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGEQR2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGEQRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGERFS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGERQ2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGERQF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGESV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGESVD()

where sigma is an m-by-n matrix which is zero except for its
min(m,n) diagonal elements, u is an m-by-m orthogonal matrix, an
are the singular values of a and the columns of u and v are the

PSGESVX()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGETF2()

permutation matrix, l is lower triangular with unit diagonal
elements (lower trapezoidal if m > n), and u is upper triangula

PSGETRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGETRI()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGETRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGGQRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSGGRQF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLABRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLACON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLACONSB()

pslaconsb looks for two consecutive small subdiagonal elements b
given by h44, h33, & h43h34 and see if this would make a

PSLACP2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLACP3()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLACPY()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLAED2()

rho    (global input/output) real
on entry, the off-diagonal element associated with the rank-
being recombined.

PSLAED3()

rho    (global input/output) real
on entry, the off-diagonal element associated with the rank-
being recombined.

PSLAEVSWP()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLAHQR()

submatrix of order 1 or 2 splits off at the bottom because a
subdiagonal element has become negligible

PSLAHRD()

pslahrd reduces the first nb columns of a real general n-by-(n-k+1)
distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that elements below th
nal similarity transformation q' * a * q. the routine returns the

PSLANGE()

pslange returns the value of the one norm, or the frobenius norm,
or the infinity norm, or the element of largest absolute value of 

PSLAPIV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLAPV2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLAQGE()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLAQSY()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLARED1D()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLARED2D()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLARFB()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLARFG()

pslarfg generates a real elementary reflector h of order n, suc

PSLARFT()

pslarft forms the triangular factor t of a real block reflector h
of order n, which is defined as a product of k elementary reflectors
if direct = 'f', h = h(1) h(2) . . . h(k) and t is upper triangular;

PSLARZB()

q is a product of k elementary reflectors as returned by pstzrzf
currently, only storev = 'r' and direct = 'b' are supported.

PSLARZT()

pslarzt forms the triangular factor t of a real block reflector
h of order > n, which is defined as a product of k elementar

PSLASCL()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLASE2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLASET()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLASMSUB()

pslasmsub looks for a small subdiagonal element from the botto

PSLASSQ()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLASWP()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLATRA()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLATRD()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLATRZ()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLAUU2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLAUUM()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSLAWIL()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSORG2L()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the last n columns of a product of k elementary reflectors of order 
q  =  h(k) . . . h(2) h(1)

PSORG2R()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the first n columns of a product of k elementary reflectors of orde

PSORGL2()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as
the first m rows of a product of k elementary reflectors of order 
q  =  h(k) . . . h(2) h(1)

PSORGLQ()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as
the first m rows of a product of k elementary reflectors of order 
q  =  h(k) . . . h(2) h(1)

PSORGQL()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the last n columns of a product of k elementary reflectors of order 
q  =  h(k) . . . h(2) h(1)

PSORGQR()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as
the first n columns of a product of k elementary reflectors of orde

PSORGR2()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the
last m rows of a product of k elementary reflectors of order 
q  =  h(1) h(2) . . . h(k)

PSORGRQ()

a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the
last m rows of a product of k elementary reflectors of order 
q  =  h(1) h(2) . . . h(k)

PSORM2L()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PSORM2R()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PSORMBR()

bidiagonal form: a(ia:*,ja:*) = q * b * p**t. q and p**t are defined
as products of elementary reflectors h(i) and g(i) respectively
let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is the

PSORMHR()

nq = m if side = 'l' and nq = n if side = 'r'. q is defined as the
product of ihi-ilo elementary reflectors, as returned by psgehrd
q = h(ilo) h(ilo+1) . . . h(ihi-1).

PSORML2()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PSORMLQ()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PSORMQL()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(k) . . . h(2) h(1)

PSORMQR()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PSORMR2()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PSORMR3()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PSORMRQ()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PSORMRZ()

where q is a real orthogonal distributed matrix defined as the
product of k elementary reflector
q = h(1) h(2) . . . h(k)

PSORMTR()

nq = m if side = 'l' and nq = n if side = 'r'. q is defined as the
product of nq-1 elementary reflectors, as returned by pssytrd
if uplo = 'u', q = h(nq-1) . . . h(2) h(1);

PSPBSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSPBTRS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSPOCON()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSPOEQU()

factors, s(i) = 1/sqrt(a(i,i)), chosen so that the scaled distri-
buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones o
of b within a factor n of the smallest possible condition number

PSPORFS()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSPOSV()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSPOSVX()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSPOTF2()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSPOTRF()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces

PSPOTRI()

vector.  this vector stores the information required to establish
the mapping between an object element and its corresponding proces