Parallel Engineering and Scientific Subroutine Library for AIX Version 2 Release 3: Guide and Reference

PDSYMM, PZSYMM, and PZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian

These subroutines compute one of the following matrix-matrix products:

1. C<--alphaAB+betaC

2. C<--alphaBA+betaC

where, in the formulas above:

A represents the global submatrix:

For side = 'L', it is A_{ia:ia+m-1,
ja:ja+m-1}.
For side = 'R', it is A_{ia:ia+n-1,
ja:ja+n-1}.

B represents the global general submatrix B_{ib:ib+m-1,
jb:jb+n-1}.

C represents the global general submatrix C_{ic:ic+m-1,
jc:jc+n-1}.

alpha and beta are scalars.

and:

For PDSYMM, submatrix A is real symmetric.
For PZSYMM, submatrix A is complex symmetric.
For PZHEMM, submatrix A is complex Hermitian.

In the following two cases, no computation is performed and the subroutine returns after doing some parameter checking:

m = 0 or n = 0
alpha is zero and beta is one.

See references [14] and [15].

Table 48. Data Types

alpha, beta, A, B, C	Subprogram
Long-precision real	PDSYMM
Long-precision complex	PZSYMM and PZHEMM

Syntax

Fortran	CALL PDSYMM \| PZSYMM \| PZHEMM (`side`, `uplo`, `m`, `n`, `alpha`, `a`, `ia`, `ja`, `desc_a`, `b`, `ib`, `jb`, `desc_b`, `beta`, `c`, `ic`, `jc`, `desc_c`)
C and C++	pdsymm \| pzsymm \| pzhemm (`side`, `uplo`, `m`, `n`, `alpha`, `a`, `ia`, `ja`, `desc_a`, `b`, `ib`, `jb`, `desc_b`, `beta`, `c`, `ic`, `jc`, `desc_c`);

On Entry

side

indicates whether A is located to the left or right of B in the equation used for this computation, where:

If side = 'L', A is to the left of B, resulting in equation 1.

If side = 'R', A is to the right of B, resulting in equation 2.

Scope: global

Specified as: a single character; side = 'L' or 'R'.

uplo

indicates whether the upper or lower triangular part of the global submatrix A is referenced, where:

If uplo = 'U', the upper triangular part is referenced.

If uplo = 'L', the lower triangular part is referenced.

Scope: global

Specified as: a single character; uplo = 'U' or 'L'.

m

is the number of rows in submatrices B and C used in the computation, and:

If side = 'L', it is the number of rows and columns in submatrix A used in the computation.

Scope: global

Specified as: a fullword integer; m >= 0.

n

is the number of columns in submatrices B and C used in the computation, and:

If side = 'R', it is the number of rows and columns in submatrix A used in the computation.

Scope: global

Specified as: a fullword integer; n >= 0.

alpha

is the scalar alpha.

Scope: global

Specified as: a number of the data type indicated in Table 48.

a

is the local part of the global real symmetric, complex symmetric, or complex Hermitian matrix A. This identifies the first element of the local array A. This subroutine computes the location of the first element of the local subarray used, based on ia, ja, desc_a, p, q, myrow, and mycol; therefore, assuming the following:

If side = 'L', numa = m

If side = 'R', numa = n

the leading LOCp(ia+numa-1) by LOCq(ja+numa-1) part of the local array A must contain the local pieces of the leading ia+numa-1 by ja+numa-1 part of the global matrix, and:

If uplo = 'U', the leading numa × numa upper triangular part of the global submatrix A_{ia:ia+numa-1,
ja:ja+numa-1} must contain the upper triangular part of the submatrix, and the strictly lower triangular part is not referenced.
If uplo = 'L', the leading numa × numa lower triangular part of the global submatrix A_{ia:ia+numa-1,
ja:ja+numa-1} must contain the lower triangular part of the submatrix, and the strictly upper triangular part is not referenced.

Scope: local

Specified as: an LLD_A by (at least) LOCq(N_A) array, containing numbers of the data type indicated in Table 48. Details about the block-cyclic data distribution of global matrix A are stored in desc_a.

ia

is the row index of the global matrix A, identifying the first row of the submatrix A.

Scope: global

Specified as: a fullword integer; 1 <= ia <= M_A and ia+numa-1 <= M_A.

ja

is the column index of the global matrix A, identifying the first column of the submatrix A.

Scope: global

Specified as: a fullword integer; 1 <= ja <= N_A and ja+numa-1 <= N_A.

desc_a

is the array descriptor for global matrix A, described in the following table:

`desc_a`	Name	Description	Limits	Scope
1	DTYPE_A	Descriptor type	DTYPE_A=1	Global
2	CTXT_A	BLACS context	Valid value, as returned by BLACS_GRIDINIT or BLACS_GRIDMAP	Global
3	M_A	Number of rows in the global matrix	If `m` = 0 and `side` = 'L' or `n` = 0 and `side` = 'R': M_A >= 0 Otherwise: M_A >= 1	Global
4	N_A	Number of columns in the global matrix	If `m` = 0 and `side` = 'L' or `n` = 0 and `side` = 'R': N_A >= 0 Otherwise: N_A >= 1	Global
5	MB_A	Row block size	MB_A >= 1	Global
6	NB_A	Column block size	NB_A >= 1	Global
7	RSRC_A	The process row of the `p` × `q` grid over which the first row of the global matrix is distributed	0 <= RSRC_A < `p`	Global
8	CSRC_A	The process column of the `p` × `q` grid over which the first column of the global matrix is distributed	0 <= CSRC_A < `q`	Global
9	LLD_A	The leading dimension of the local array	LLD_A >= max(1,LOCp(M_A))	Local

Specified as: an array of (at least) length 9, containing fullword integers.

b

is the local part of the global general matrix B. This identifies the first element of the local array B. This subroutine computes the location of the first element of the local subarray used, based on ib, jb, desc_b, p, q, myrow, and mycol; therefore, the leading LOCp(ib+m-1) by LOCq(jb+n-1) part of the local array B must contain the local pieces of the leading ib+m-1 by jb+n-1 part of the global matrix.

Scope: local

Specified as: an LLD_B by (at least) LOCq(N_B) array, containing numbers of the data type indicated in Table 48. Details about the block-cyclic data distribution of global matrix B are stored in desc_b.

ib

is the row index of the global matrix B, identifying the first row of the submatrix B.

Scope: global

Specified as: a fullword integer; 1 <= ib <= M_B and ib+m-1 <= M_B.

jb

is the column index of the global matrix B, identifying the first column of the submatrix B.

Scope: global

Specified as: a fullword integer; 1 <= jb <= N_B and jb+n-1 <= N_B.

desc_b

is the array descriptor for global matrix B, described in the following table:

`desc_b`	Name	Description	Limits	Scope
1	DTYPE_B	Descriptor type	DTYPE_B=1	Global
2	CTXT_B	BLACS context	Valid value, as returned by BLACS_GRIDINIT or BLACS_GRIDMAP	Global
3	M_B	Number of rows in the global matrix	If `m` = 0 or `n` = 0: M_B >= 0 Otherwise: M_B >= 1	Global
4	N_B	Number of columns in the global matrix	If `m` = 0 or `n` = 0: N_B >= 0 Otherwise: N_B >= 1	Global
5	MB_B	Row block size	MB_B >= 1	Global
6	NB_B	Column block size	NB_B >= 1	Global
7	RSRC_B	The process row of the `p` × `q` grid over which the first row of the global matrix is distributed	0 <= RSRC_B < `p`	Global
8	CSRC_B	The process column of the `p` × `q` grid over which the first column of the global matrix is distributed	0 <= CSRC_B < `q`	Global
9	LLD_B	The leading dimension of the local array	LLD_B >= max(1,LOCp(M_B))	Local

Specified as: an array of (at least) length 9, containing fullword integers.

beta

is the scalar beta.

Scope: global

Specified as: a number of the data type indicated in Table 48.

c

is the local part of the global general matrix C. This identifies the first element of the local array C. This subroutine computes the location of the first element of the local subarray used, based on ic, jc, desc_c, p, q, myrow, and mycol; therefore, the leading LOCp(ic+m-1) by LOCq(jc+n-1) part of the local array C must contain the local pieces of the leading ic+m-1 by jc+n-1 part of the global matrix.

When beta is zero, C need not be set on input.

Scope: local

Specified as: an LLD_C by (at least) LOCq(N_C) array, containing numbers of the data type indicated in Table 48. Details about the block-cyclic data distribution of global matrix C are stored in desc_c.

ic

is the row index of the global matrix C, identifying the first row of the submatrix C.

Scope: global

Specified as: a fullword integer; 1 <= ic <= M_C and ic+m-1 <= M_C.

jc

is the column index of the global matrix C, identifying the first column of the submatrix C.

Scope: global

Specified as: a fullword integer; 1 <= jc <= N_C and jc+n-1 <= N_C.

desc_c

is the array descriptor for global matrix C, described in the following table:

`desc_c`	Name	Description	Limits	Scope
1	DTYPE_C	Descriptor type	DTYPE_C=1	Global
2	CTXT_C	BLACS context	Valid value, as returned by BLACS_GRIDINIT or BLACS_GRIDMAP	Global
3	M_C	Number of rows in the global matrix	If `m` = 0 or `n` = 0: M_C >= 0 Otherwise: M_C >= 1	Global
4	N_C	Number of columns in the global matrix	If `m` = 0 or `n` = 0: N_C >= 0 Otherwise: N_C >= 1	Global
5	MB_C	Row block size	MB_C >= 1	Global
6	NB_C	Column block size	NB_C >= 1	Global
7	RSRC_C	The process row of the `p` × `q` grid over which the first row of the global matrix is distributed	0 <= RSRC_C < `p`	Global
8	CSRC_C	The process column of the `p` × `q` grid over which the first column of the global matrix is distributed	0 <= CSRC_C < `q`	Global
9	LLD_C	The leading dimension of the local array	LLD_C >= max(1,LOCp(M_C))	Local

Specified as: an array of (at least) length 9, containing fullword integers.

On Return

c

is the updated local part of the global matrix C, containing the results of the computation.

Scope: local

Returned as: an LLD_C by (at least) LOCq(N_C) array, containing numbers of the data type indicated in Table 48.

Notes and Coding Rules

These subroutines accept lowercase letters for the side and uplo arguments.
The matrices must have no common elements; otherwise, results are unpredictable.
The imaginary parts of the diagonal elements of a complex Hermitian matrix A are assumed to be zero, so you do not have to set these values.
The NUMROC utility subroutine can be used to determine the values of LOCp(M_) and LOCq(N_) used in the argument descriptions above. For details, see Determining the Number of Rows and Columns in Your Local Arrays and NUMROC--Compute the Number of Rows or Columns of a Block-Cyclically Distributed Matrix Contained in a Process.
For suggested block sizes, see Coding Tips for Optimizing Parallel Performance.
The following values must be equal: CTXT_A = CTXT_B = CTXT_C.
If side = 'L':
- In the process grid, the process row containing the first row of the submatrix A must also contain the first row of the submatrices B and C; that is:
  
  iarow = ibrow
  iarow = icrow
  where:
  
  iarow = mod((((ia-1)/MB_A)+RSRC_A), p)
  ibrow = mod((((ib-1)/MB_B)+RSRC_B), p)
  icrow = mod((((ic-1)/MB_C)+RSRC_C), p)
- If looping is required--that is, either of the following is true:
  
  n+mod(jb-1, NB_B) > NB_B
  n+mod(jc-1, NB_C) > NB_C
  
  then:
  - The following block sizes must be equal: NB_B = NB_C.
  - The block column offset of B must be equal to the block column offset of C; that is, mod(jb-1, NB_B) = mod(jc-1, NB_C).
If side = 'R':
- In the process grid, the process column containing the first column of the submatrix A must also contain the first column of the submatrices B and C; that is:
  
  iacol = ibcol
  iacol = iccol
  where:
  
  iacol = mod((((ja-1)/NB_A)+CSRC_A), q)
  ibcol = mod((((jb-1)/NB_B)+CSRC_B), q)
  iccol = mod((((jc-1)/NB_C)+CSRC_C), q)
- If looping is required--that is, either of the following is true:
  
  m+mod(ib-1, MB_B) > MB_B
  m+mod(ic-1, MB_C) > MB_C
  
  then:
  - The following block sizes must be equal: MB_B = MB_C.
  - The block row offset of B must be equal to the block row offset of C; that is, mod(ib-1, MB_B) = mod(ic-1, MB_C)
If all the following are true:
- A is contained within a single block, that is:
  
  numa+mod(ia-1, MB_A) <= MB_A
  numa+mod(ja-1, NB_A) <= NB_A
  where:
  
  If side = 'L', numa = m
  If side = 'R', numa = n
- If side = 'L', then (in the process grid) the process column containing the first column of the submatrix B must also contain the first column of the submatrix C, that is, ibcol = iccol, where:
  
  ibcol = mod((((jb-1)/NB_B)+CSRC_B), q)
  iccol = mod((((jc-1)/NB_C)+CSRC_C), q)
- If side = 'R', then (in the process grid) the process row containing the first row of the submatrix B must also contain the first row of the submatrix C; that is, ibrow = icrow, where:
  
  ibrow = mod((((ib-1)/MB_B)+RSRC_B), p)
  icrow = mod((((ic-1)/MB_C)+RSRC_C), p)
then you must follow these rules:
- If side = 'L', then B and C must be block row matrices; that is, if p > 1:
  
  m+mod(ib-1, MB_B) <= MB_B
  m+mod(ic-1, MB_C) <= MB_C
- If side = 'R', then B and C must be block column matrices; that is, if q > 1:
  
  n+mod(jb-1, NB_B) <= NB_B
  n+mod(jc-1, NB_C) <= NB_C
If the following is true:
- A is not contained within a single block.
or if all the following are true:
- A is contained within a single block.
- If side = 'L', then (in the process grid) the process column containing the first column of the submatrix B does not contain the first column of the submatrix C, that is, ibcol <> iccol, where:
  
  ibcol = mod((((jb-1)/NB_B)+CSRC_B), q)
  iccol = mod((((jc-1)/NB_C)+CSRC_C), q)
- If side = 'R', then (in the process grid) the process row containing the first row of the submatrix B does not contain the first row of the submatrix C; that is, ibrow <> icrow, where:
  
  ibrow = mod((((ib-1)/MB_B)+RSRC_B), p)
  icrow = mod((((ic-1)/MB_C)+RSRC_C), p)
then you must follow these rules:
- The global matrix A must be distributed using a square block-cyclic distribution; that is, MB_A = NB_A.
- The global matrix A must be aligned on a block boundary, that is:
  
  ia-1 must be a multiple of MB_A.
  ja-1 must be a multiple of NB_A.
- If side = 'L':
  - The following block sizes must be equal: MB_B = MB_C = NB_A.
  - The global matrices B and C must be aligned on a block row boundary, that is:
    
    ib-1 must be a multiple of MB_B.
    ic-1 must be a multiple of MB_C.
- If side = 'R':
  - The following block sizes must be equal: NB_B = NB_C = MB_A.
  - The global matrices B and C must be aligned on a block column boundary, that is:
    
    jb-1 must be a multiple of NB_B.
    jc-1 must be a multiple of NB_C.

DTYPE_A is invalid.
DTYPE_B is invalid.
DTYPE_C is invalid.

Stage 2:

CTXT_A is invalid.

Stage 3:

This subroutine was called from outside the process grid.

Stage 4:

side <> 'L' or 'R'
uplo <> 'U' or 'L'
m < 0
n < 0
M_A < 0 and m = 0 and side = 'L'; M_A < 0 and n = 0 and side = 'R'; M_A < 1 otherwise
N_A < 0 and m = 0 and side = 'L'; N_A < 0 and n = 0 and side = 'R'; N_A < 1 otherwise
MB_A < 1
NB_A < 1
RSRC_A < 0 or RSRC_A >= p
CSRC_A < 0 or CSRC_A >= q
ia < 1
ja < 1
M_B < 0 and (m = 0 or n = 0); M_B < 1 otherwise
N_B < 0 and (m = 0 or n = 0); N_B < 1 otherwise
MB_B < 1
NB_B < 1
RSRC_B < 0 or RSRC_B >= p
CSRC_B < 0 or CSRC_B >= q
ib < 1
jb < 1
M_C < 0 and (m = 0 or n = 0); M_C < 1 otherwise
N_C < 0 and (m = 0 or n = 0); N_C < 1 otherwise
MB_C < 1
NB_C < 1
RSRC_C < 0 or RSRC_C >= p
CSRC_C < 0 or CSRC_C >= q
ic < 1
jc < 1
CTXT_A <> CTXT_B
CTXT_A <> CTXT_C

Stage 5: If (m <> 0 or side <> 'L') and (n <> 0 or side <> 'R'):

ia > M_A
ja > N_A
ia+numa-1 > M_A
ja+numa-1 > N_A
where numa = m if side = 'L' and numa = n if side = 'R'.

If m <> 0 and n <> 0:

ib > M_B
jb > N_B
ib+m-1 > M_B
jb+n-1 > N_B
ic > M_C
jc > N_C
ic+m-1 > M_C
jc+n-1 > N_C

Stage 6: If A is contained within a single block, that is:

numa+mod(ia-1, MB_A) <= MB_A

numa+mod(ja-1, NB_A) <= NB_A

where:

If side = 'L', numa = m

If side = 'R', numa = n

and:

If side = 'L', then (in the process grid) the process column containing the first column of the submatrix B must also contain the first column of the submatrix C, that is, ibcol = iccol, where:

ibcol = mod((((jb-1)/NB_B)+CSRC_B), q)
iccol = mod((((jc-1)/NB_C)+CSRC_C), q)
If side = 'R', then (in the process grid) the process row containing the first row of the submatrix B must also contain the first row of the submatrix C; that is, ibrow = icrow, where:

ibrow = mod((((ib-1)/MB_B)+RSRC_B), p)
icrow = mod((((ic-1)/MB_C)+RSRC_C), p)

then:

If side = 'L':
1. p > 1 and m+mod(ib-1, MB_B) > MB_B
2. p > 1 and m+mod(ic-1, MB_C) > MB_C
If side = 'R':
1. q > 1 and n+mod(jb-1, NB_B) > NB_B
2. q > 1 and n+mod(jc-1, NB_C) > NB_C

If A is not contained within a single block, or if A is contained within a single block and:

If side = 'L', then (in the process grid) the process column containing the first column of the submatrix B does not contain the first column of the submatrix C, that is, ibcol <> iccol, where:

ibcol = mod((((jb-1)/NB_B)+CSRC_B), q)
iccol = mod((((jc-1)/NB_C)+CSRC_C), q)
If side = 'R', then (in the process grid) the process row containing the first row of the submatrix B does not contain the first row of the submatrix C; that is, ibrow <> icrow, where:

ibrow = mod((((ib-1)/MB_B)+RSRC_B), p)
icrow = mod((((ic-1)/MB_C)+RSRC_C), p)

then:

MB_A <> NB_A
mod(ia-1, MB_A) <> 0
mod(ja-1, NB_A) <> 0

If side = 'L':
MB_B <> NB_A
MB_C <> NB_A
mod(ib-1, MB_B) <> 0
mod(ic-1, MB_C) <> 0

If side = 'R':
NB_B <> MB_A
NB_C <> MB_A
mod(jb-1, NB_B) <> 0
mod(jc-1, NB_C) <> 0

In all cases:

LLD_A < max(1, LOCp(M_A))
LLD_B < max(1, LOCp(M_B))
LLD_C < max(1, LOCp(M_C))

If side = 'L' and looping is required--that is, either of the following is true:

n+mod(jb-1, NB_B) > NB_B
n+mod(jc-1, NB_C) > NB_C

then:
NB_B <> NB_C
mod(jb-1, NB_B) <> mod(jc-1, NB_C).

If side = 'L':
In the process grid, the process row containing the first row of the submatrix A does not contain the first row of the submatrix B; that is, iarow <> ibrow, where:

iarow = mod((((ia-1)/MB_A)+RSRC_A), p)
ibrow = mod((((ib-1)/MB_B)+RSRC_B), p)
In the process grid, the process row containing the first row of the submatrix A does not contain the first row of the submatrix C; that is, iarow <> icrow, where:

iarow = mod((((ia-1)/MB_A)+RSRC_A), p)
icrow = mod((((ic-1)/MB_C)+RSRC_C), p)

If side = 'R' and looping is required--that is, either of the following is true:

m+mod(ib-1, MB_B) > MB_B
m+mod(ic-1, MB_C) > MB_C

then:
MB_B <> MB_C
mod(ib-1, MB_B) <> mod(ic-1, MB_C).

If side = 'R':
In the process grid, the process column containing the first column of the submatrix A does not contain the first column of the submatrix B; that is, iacol <> ibcol, where:

iacol = mod((((ja-1)/NB_A)+CSRC_A), q)
ibcol = mod((((jb-1)/NB_B)+CSRC_B), q)
In the process grid, the process column containing the first column of the submatrix A does not contain the first column of the submatrix C; that is, iacol <> iccol, where:

iacol = mod((((ja-1)/NB_A)+CSRC_A), q)
iccol = mod((((jc-1)/NB_C)+CSRC_C), q)

Example 1

This example computes C = betaC+alphaBA using a 2 × 2 process grid.

Call Statements and Input

 ORDER = 'R'
 NPROW = 2
 NPCOL = 2
 CALL BLACS_GET(0, 0, ICONTXT)
 CALL BLACS_GRIDINIT(ICONTXT, ORDER, NPROW, NPCOL)
 CALL BLACS_GRIDINFO(ICONTXT, NPROW, NPCOL, MYROW, MYCOL)
 
              SIDE  UPLO   M   N    ALPHA    A  IA  JA   DESC_A   B  IB   JB
               |     |     |   |      |      |   |   |     |      |   |   |
 CALL PDSYMM( 'R' , 'U' , 16 , 8 ,  1.0D0  , A , 1 , 1 , DESC_A , B , 1 , 1 ,
 
              DESC_B   BETA    C  IC  JC   DESC_C
                |        |     |   |   |     |
              DESC_B , 0.0D0 , C , 1 , 1 , DESC_C )

	Desc_A	Desc_B	Desc_C
DTYPE_	1	1	1
CTXT_	`icontxt`^(IOBG20)	`icontxt`^(IOBG20)	`icontxt`^(IOBG20)
M_	8	16	16
N_	8	8	8
MB_	2	4	4
NB_	2	2	2
RSRC_	0	0	0
CSRC_	0	0	0
LLD_	See below^(EPSSL20)	See below^(EPSSL20)	See below^(EPSSL20)
Notes: `icontxt` is the output of the BLACS_GRIDINIT call. Each process should set the LLD_ as follows: LLD_A = MAX(1,NUMROC(M_A, MB_A, MYROW, RSRC_A, NPROW)) LLD_B = MAX(1,NUMROC(M_B, MB_B, MYROW, RSRC_B, NPROW)) LLD_C = MAX(1,NUMROC(M_C, MB_C, MYROW, RSRC_C, NPROW)) In this example, LLD_A = 4 on all processes, and LLD_B = LLD_C = 8 on all processes.

Global real symmetric matrix A of order 8 with block size 2 × 2:

B,D        0             1             2             3
     *                                                     *
 0   |  0.0 -1.0  |  -1.0  0.0  |   0.0  0.0  |   0.0  0.0 |
     |   .   1.0  |   0.0  1.0  |   0.0  1.0  |   0.0  1.0 |
     | -----------|-------------|-------------|----------- |
 1   |   .   .    |  -1.0 -1.0  |   0.0  0.0  |   1.0  0.0 |
     |   .   .    |    .  -1.0  |   1.0  1.0  |   0.0  1.0 |
     | -----------|-------------|-------------|----------- |
 2   |   .    .   |    .    .   |  -1.0  0.0  |   0.0  0.0 |
     |   .    .   |    .    .   |    .   1.0  |   0.0  0.0 |
     | -----------|-------------|-------------|----------- |
 3   |   .    .   |    .    .   |    .    .   |   0.0  0.0 |
     |   .    .   |    .    .   |    .    .   |    .   0.0 |
     *                                                     *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for A:

p,q  |          0           |           1
-----|----------------------|----------------------
     |  0.0 -1.0  0.0  0.0  |  -1.0  0.0  0.0  0.0
     |   .   1.0  0.0  1.0  |   0.0  1.0  0.0  1.0
 0   |   .    .  -1.0  0.0  |    .    .   0.0  0.0
     |   .    .    .   1.0  |    .    .   0.0  0.0
-----|----------------------|----------------------
     |   .    .   0.0  0.0  |  -1.0 -1.0  1.0  0.0
     |   .    .   1.0  1.0  |    .  -1.0  0.0  1.0
 1   |   .    .    .    .   |    .    .   0.0  0.0
     |   .    .    .    .   |    .    .    .   0.0

Global general 16 × 8 matrix B with block size 4 × 2:

B,D        0             1             2             3
     *                                                     *
     | -1.0  0.0  |   1.0 -1.0  |   1.0  1.0  |  -1.0 -1.0 |
     | -1.0 -1.0  |   1.0  0.0  |   1.0 -1.0  |  -1.0  1.0 |
 0   |  1.0  1.0  |  -1.0  0.0  |  -1.0  0.0  |   1.0  0.0 |
     |  0.0 -1.0  |   0.0  0.0  |   0.0  0.0  |   0.0 -1.0 |
     | -----------|-------------|-------------|----------- |
     |  0.0  1.0  |   0.0  1.0  |   0.0  1.0  |   1.0  0.0 |
     |  0.0  0.0  |   1.0  0.0  |  -1.0 -1.0  |   0.0  0.0 |
 1   |  1.0  1.0  |   0.0  0.0  |   1.0  1.0  |   0.0 -1.0 |
     |  0.0  0.0  |  -1.0  0.0  |   0.0  1.0  |   0.0  1.0 |
     | -----------|-------------|-------------|----------- |
     |  0.0  0.0  |   0.0 -1.0  |   1.0  1.0  |   0.0  1.0 |
     | -1.0 -1.0  |   1.0  0.0  |   0.0 -1.0  |   0.0  1.0 |
 2   |  0.0  0.0  |   0.0  1.0  |   1.0  0.0  |   0.0  0.0 |
     |  0.0  0.0  |   1.0  1.0  |   0.0 -1.0  |   0.0  0.0 |
     | -----------|-------------|-------------|----------- |
     |  1.0  1.0  |  -1.0  0.0  |  -1.0 -1.0  |   1.0  1.0 |
     |  0.0  0.0  |   0.0  0.0  |   1.0  0.0  |   0.0 -1.0 |
 3   |  0.0  1.0  |   0.0  0.0  |   0.0  0.0  |   0.0  0.0 |
     | -1.0  0.0  |  -1.0  0.0  |   0.0  1.0  |   1.0  0.0 |
     *                                                     *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for B:

p,q  |          0           |           1
-----|----------------------|----------------------
     | -1.0  0.0  1.0  1.0  |   1.0 -1.0 -1.0 -1.0
     | -1.0 -1.0  1.0 -1.0  |   1.0  0.0 -1.0  1.0
     |  1.0  1.0 -1.0  0.0  |  -1.0  0.0  1.0  0.0
     |  0.0 -1.0  0.0  0.0  |   0.0  0.0  0.0 -1.0
 0   |  0.0  0.0  1.0  1.0  |   0.0 -1.0  0.0  1.0
     | -1.0 -1.0  0.0 -1.0  |   1.0  0.0  0.0  1.0
     |  0.0  0.0  1.0  0.0  |   0.0  1.0  0.0  0.0
     |  0.0  0.0  0.0 -1.0  |   1.0  1.0  0.0  0.0
-----|----------------------|----------------------
     |  0.0  1.0  0.0  1.0  |   0.0  1.0  1.0  0.0
     |  0.0  0.0 -1.0 -1.0  |   1.0  0.0  0.0  0.0
     |  1.0  1.0  1.0  1.0  |   0.0  0.0  0.0 -1.0
     |  0.0  0.0  0.0  1.0  |  -1.0  0.0  0.0  1.0
 1   |  1.0  1.0 -1.0 -1.0  |  -1.0  0.0  1.0  1.0
     |  0.0  0.0  1.0  0.0  |   0.0  0.0  0.0 -1.0
     |  0.0  1.0  0.0  0.0  |   0.0  0.0  0.0  0.0
     | -1.0  0.0  0.0  1.0  |  -1.0  0.0  1.0  0.0

Output:

Global general 16 × 8 matrix C with block size 4 × 2:

B,D        0             1             2             3
     *                                                     *
     | -1.0  0.0  |   0.0  1.0  |  -2.0  0.0  |   1.0 -1.0 |
     |  0.0  0.0  |  -1.0 -1.0  |  -1.0 -2.0  |   1.0 -1.0 |
 0   |  0.0  0.0  |   1.0  1.0  |   1.0  1.0  |  -1.0  1.0 |
     |  1.0 -2.0  |   0.0 -2.0  |   0.0 -1.0  |   0.0 -1.0 |
     | -----------|-------------|-------------|----------- |
     | -1.0  3.0  |   0.0  1.0  |   1.0  3.0  |   0.0  2.0 |
     | -1.0 -1.0  |  -1.0 -3.0  |   1.0 -1.0  |   1.0  0.0 |
 1   | -1.0  0.0  |  -1.0  2.0  |  -1.0  2.0  |   0.0  1.0 |
     |  1.0  2.0  |   1.0  3.0  |   0.0  1.0  |  -1.0  0.0 |
     | -----------|-------------|-------------|----------- |
     |  0.0  1.0  |   1.0  4.0  |  -2.0  0.0  |   0.0 -1.0 |
     |  0.0  0.0  |   0.0 -2.0  |   0.0 -2.0  |   1.0 -1.0 |
 2   |  0.0  1.0  |  -1.0  0.0  |   0.0  1.0  |   0.0  1.0 |
     | -1.0  0.0  |  -2.0 -3.0  |   1.0  0.0  |   1.0  1.0 |
     | -----------|-------------|-------------|----------- |
     |  0.0  0.0  |   1.0  1.0  |   1.0  0.0  |  -1.0  1.0 |
     |  0.0 -1.0  |   0.0  0.0  |  -1.0  0.0  |   0.0  0.0 |
 3   | -1.0  1.0  |   0.0  1.0  |   0.0  1.0  |   0.0  1.0 |
     |  1.0  2.0  |   3.0  2.0  |   0.0  1.0  |  -1.0  0.0 |
     *                                                     *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for C:

p,q  |          0           |           1
-----|----------------------|----------------------
     | -1.0  0.0 -2.0  0.0  |   0.0  1.0  1.0 -1.0
     |  0.0  0.0 -1.0 -2.0  |  -1.0 -1.0  1.0 -1.0
     |  0.0  0.0  1.0  1.0  |   1.0  1.0 -1.0  1.0
     |  1.0 -2.0  0.0 -1.0  |   0.0 -2.0  0.0 -1.0
 0   |  0.0  1.0 -2.0  0.0  |   1.0  4.0  0.0 -1.0
     |  0.0  0.0  0.0 -2.0  |   0.0 -2.0  1.0 -1.0
     |  0.0  1.0  0.0  1.0  |  -1.0  0.0  0.0  1.0
     | -1.0  0.0  1.0  0.0  |  -2.0 -3.0  1.0  1.0
-----|----------------------|----------------------
     | -1.0  3.0  1.0  3.0  |   0.0  1.0  0.0  2.0
     | -1.0 -1.0  1.0 -1.0  |  -1.0 -3.0  1.0  0.0
     | -1.0  0.0 -1.0  2.0  |  -1.0  2.0  0.0  1.0
     |  1.0  2.0  0.0  1.0  |   1.0  3.0 -1.0  0.0
 1   |  0.0  0.0  1.0  0.0  |   1.0  1.0 -1.0  1.0
     |  0.0 -1.0 -1.0  0.0  |   0.0  0.0  0.0  0.0
     | -1.0  1.0  0.0  1.0  |   0.0  1.0  0.0  1.0
     |  1.0  2.0  0.0  1.0  |   3.0  2.0 -1.0  0.0

Example 2

This example computes C = betaC+alphaBA using a 2 × 2 process grid.

Call Statements and Input

 ORDER = 'R'
 NPROW = 2
 NPCOL = 2
 CALL BLACS_GET(0, 0, ICONTXT)
 CALL BLACS_GRIDINIT(ICONTXT, ORDER, NPROW, NPCOL)
 CALL BLACS_GRIDINFO(ICONTXT, NPROW, NPCOL, MYROW, MYCOL)
 
              SIDE  UPLO   M   N     ALPHA     A  IA  JA   DESC_A   B  IB   JB
               |     |     |   |       |       |   |   |    |       |   |   |
 CALL PZSYMM( 'R' , 'U' , 16 , 8 ,   ALPHA   , A , 1 , 1 , DESC_A , B , 1 , 1 ,
 
              DESC_B    BETA     C  IC  JC   DESC_C
                |         |      |   |   |    |
              DESC_B ,  BETA   , C , 1 , 1 , DESC_C )
 
              ALPHA  =  (1.0, 2.0)
 
              BETA   =  (0.0, 0.0)

	Desc_A	Desc_B	Desc_C
DTYPE_	1	1	1
CTXT_	`icontxt`^(IOBG21)	`icontxt`^(IOBG21)	`icontxt`^(IOBG21)
M_	8	16	16
N_	8	8	8
MB_	2	4	4
NB_	2	2	2
RSRC_	0	0	0
CSRC_	0	0	0
LLD_	See below^(EPSSL21)	See below^(EPSSL21)	See below^(EPSSL21)
Notes: `icontxt` is the output of the BLACS_GRIDINIT call. Each process should set the LLD_ as follows: LLD_A = MAX(1,NUMROC(M_A, MB_A, MYROW, RSRC_A, NPROW)) LLD_B = MAX(1,NUMROC(M_B, MB_B, MYROW, RSRC_B, NPROW)) LLD_C = MAX(1,NUMROC(M_C, MB_C, MYROW, RSRC_C, NPROW)) In this example, LLD_A = 4 on all processes, and LLD_B = LLD_C = 8 on all processes.

Global complex symmetric matrix A of order 8 with block size 2 × 2:

B,D          0                         1                        2                         3
     *                                                                                                      *
 0   | ( 0.0, 1.0) (-1.0, 0.0) | (-1.0, 0.0) ( 0.0, 1.0) |( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 0.0, 1.0) |
     |      .      ( 1.0, 2.0) | ( 0.0, 1.0) ( 1.0, 2.0) |( 0.0, 1.0) ( 1.0, 2.0) | ( 0.0, 1.0) ( 1.0, 2.0) |
     | ------------------------|-------------------------|------------------------|------------------------ |
 1   |      .           .      | (-1.0, 0.0) (-1.0, 0.0) |( 0.0, 1.0) ( 0.0, 1.0) | ( 1.0, 2.0) ( 0.0, 1.0) |
     |      .           .      |      .      (-1.0, 0.0) |( 1.0, 2.0) ( 1.0, 2.0) | ( 0.0, 1.0) ( 1.0, 2.0) |
     | ------------------------|-------------------------|------------------------|------------------------ |
 2   |      .           .      |      .           .      |(-1.0, 0.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 0.0, 1.0) |
     |      .           .      |      .           .      |     .      ( 1.0, 2.0) | ( 0.0, 1.0) ( 0.0, 1.0) |
     | ------------------------|-------------------------|------------------------|------------------------ |
 3   |      .           .      |      .           .      |     .           .      | ( 0.0, 1.0) ( 0.0, 1.0) |
     |      .           .      |      .           .      |     .           .      |      .      ( 0.0, 1.0) |
     *                                                                                                      *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for A:

p,q  |                        0                                                 1
-----|-------------------------------------------------|-------------------------------------------------
     | ( 0.0, 1.0) (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0) | (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0)
     |      .      ( 1.0, 2.0) ( 0.0, 1.0) ( 1.0, 2.0) | ( 0.0, 1.0) ( 1.0, 2.0) ( 0.0, 1.0) ( 1.0, 2.0)
 0   |      .           .      (-1.0, 0.0) ( 0.0, 1.0) |      .           .      ( 0.0, 1.0) ( 0.0, 1.0)
     |      .           .           .      ( 1.0, 2.0) |      .           .      ( 0.0, 1.0) ( 0.0, 1.0)
-----|-------------------------------------------------|-------------------------------------------------
     |      .           .      ( 0.0, 1.0) ( 0.0, 1.0) | (-1.0, 0.0) (-1.0, 0.0) ( 1.0, 2.0) ( 0.0, 1.0)
     |      .           .      ( 1.0, 2.0) ( 1.0, 2.0) |      .      (-1.0, 0.0) ( 0.0, 1.0) ( 1.0, 2.0)
 1   |      .           .           .           .      |      .           .      ( 0.0, 1.0) ( 0.0, 1.0)
     |      .           .           .           .      |      .           .           .      ( 0.0, 1.0)

Global general 16 × 8 matrix B with block size 4 × 2:

B,D               0                         1                         2                         3
     *                                                                                                       *
     | (-1.0,-3.0) ( 0.0,-2.0) | ( 1.0,-1.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 1.0,-1.0) | (-1.0,-3.0) (-1.0,-3.0) |
     | (-1.0,-3.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 1.0,-1.0) (-1.0,-3.0) | (-1.0,-3.0) ( 1.0,-1.0) |
 0   | ( 1.0,-1.0) ( 1.0,-1.0) | (-1.0,-3.0) ( 0.0,-2.0) | (-1.0,-3.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 0.0,-2.0) |
     | ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) (-1.0,-3.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 0.0,-2.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 1.0,-1.0) | ( 1.0,-1.0) ( 0.0,-2.0) |
     | ( 0.0,-2.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 0.0,-2.0) | (-1.0,-3.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
 1   | ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) (-1.0,-3.0) |
     | ( 0.0,-2.0) ( 0.0,-2.0) | (-1.0,-3.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 1.0,-1.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 1.0,-1.0) |
     | (-1.0,-3.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 1.0,-1.0) |
 2   | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 1.0,-1.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
     | ( 0.0,-2.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 1.0,-1.0) ( 1.0,-1.0) | (-1.0,-3.0) ( 0.0,-2.0) | (-1.0,-3.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 1.0,-1.0) |
     | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) (-1.0,-3.0) |
 3   | ( 0.0,-2.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
     | (-1.0,-3.0) ( 0.0,-2.0) | (-1.0,-3.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 1.0,-1.0) | ( 1.0,-1.0) ( 0.0,-2.0) |
     *                                                                                                       *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for B:

p,q  |                        0                        |                        1
-----|-------------------------------------------------|-------------------------------------------------
     | (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 1.0,-1.0) | ( 1.0,-1.0) (-1.0,-3.0) (-1.0,-3.0) (-1.0,-3.0)
     | (-1.0,-3.0) (-1.0,-3.0) ( 1.0,-1.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 0.0,-2.0) (-1.0,-3.0) ( 1.0,-1.0)
     | ( 1.0,-1.0) ( 1.0,-1.0) (-1.0,-3.0) ( 0.0,-2.0) | (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0)
     | ( 0.0,-2.0) (-1.0,-3.0) ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) (-1.0,-3.0)
 0   | ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) (-1.0.-3.0) ( 0.0,-2.0) ( 1.0,-1.0)
     | (-1.0,-3.0) (-1.0,-3.0) ( 0.0,-2.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0)
     | ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0)
     | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0)
-----|-------------------------------------------------|-------------------------------------------------
     | ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 1.0,-1.0) ( 1.0,-1.0) ( 0.0,-2.0)
     | ( 0.0,-2.0) ( 0.0,-2.0) (-1.0,-3.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0)
     | ( 1.0,-1.0) ( 1.0,-1.0) ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) (-1.0,-3.0)
     | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0) | (-1.0,-3.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0)
 1   | ( 1.0,-1.0) ( 1.0,-1.0) (-1.0,-3.0) (-1.0,-3.0) | (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 1.0,-1.0)
     | ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) (-1.0,-3.0)
     | ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0)
     | (-1.0,-3.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0) | (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0)

Output:

Global general 16 × 8 matrix C with block size 4 × 2:

B,D               0                         1                         2                         3
     *                                                                                                       *
     | (11.0,27.0) (37.0,39.0) | ( 7.0,29.0) (27.0,39.0) | (27.0,29.0) (37.0,39.0) | (21.0,37.0) (35.0,35.0) |
     | ( 7.0,29.0) (37.0,39.0) | (11.0,27.0) (35.0,35.0) | (23.0,31.0) (45.0,35.0) | (21.0,37.0) (35.0,35.0) |
 0   | ( 1.0,27.0) (31.0,37.0) | (-3.0,29.0) (21.0,37.0) | ( 9.0,33.0) (27.0,39.0) | (23.0,31.0) (21.0,37.0) |
     | ( 6.0,32.0) (48.0,36.0) | (10.0,30.0) (42.0,34.0) | (22.0,34.0) (44.0,38.0) | (28.0,36.0) (38.0,36.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | (-4.0,22.0) (10.0,40.0) | (-8.0,24.0) (12.0,34.0) | ( 0.0,30.0) (10.0,40.0) | (10.0,30.0) ( 8.0,36.0) |
     | (11.0,27.0) (41.0,37.0) | (11.0,27.0) (43.0,31.0) | (15.0,35.0) (41.0,37.0) | (21.0,37.0) (31.0,37.0) |
 1   | (-1.0,23.0) (25.0,35.0) | (-1.0,23.0) (11.0,37.0) | (11.0,27.0) (17.0,39.0) | (13.0,31.0) (15.0,35.0) |
     | (-3.0,29.0) (23.0,41.0) | (-3.0,29.0) (13.0,41.0) | (13.0,31.0) (27.0,39.0) | (23.0,31.0) (25.0,35.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | (-2.0,26.0) (24.0,38.0) | (-6.0,28.0) ( 6.0,42.0) | (18.0,26.0) (28.0,36.0) | (16.0,32.0) (26.0,32.0) |
     | ( 7.0,29.0) (37.0,39.0) | ( 7.0,29.0) (39.0,33.0) | (19.0,33.0) (45.0,35.0) | (21.0,37.0) (35.0,35.0) |
 2   | (-2.0,26.0) (24.0,38.0) | ( 2.0,24.0) (22.0,34.0) | (10.0,30.0) (24.0,38.0) | (16.0,32.0) (18.0,36.0) |
     | ( 5.0,25.0) (31.0,37.0) | ( 9.0,23.0) (37.0,29.0) | ( 9.0,33.0) (31.0,37.0) | (15.0,35.0) (21.0,37.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 1.0,27.0) (31.0,37.0) | (-3.0,29.0) (21.0,37.0) | ( 9.0,33.0) (31.0,37.0) | (23.0,31.0) (21.0,37.0) |
     | ( 4.0,28.0) (38.0,36.0) | ( 4.0,28.0) (28.0,36.0) | (20.0,30.0) (34.0,38.0) | (22.0,34.0) (28.0,36.0) |
 3   | ( 5.0,25.0) (27.0,39.0) | ( 1.0,27.0) (21.0,37.0) | (13.0,31.0) (27.0,39.0) | (19.0,33.0) (21.0,37.0) |
     | ( 0.0,30.0) (26.0,42.0) | (-8.0,34.0) (20.0,40.0) | (16.0,32.0) (30.0,40.0) | (26.0,32.0) (28.0,36.0) |
     *                                                                                                       *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for C:

p,q  |                        0                        |                        1
-----|-------------------------------------------------|-------------------------------------------------
     | (11.0,27.0) (37.0,39.0) (27.0,29.0) (37.0,39.0) | ( 7.0,29.0) (27.0,39.0) (21.0,37.0) (35.0,35.0)
     | ( 7.0,29.0) (37.0,39.0) (23.0,31.0) (45.0,35.0) | (11.0,27.0) (35.0,35.0) (21.0,37.0) (35.0,35.0)
     | ( 1.0,27.0) (31.0,37.0) ( 9.0,33.0) (27.0,39.0) | (-3.0,29.0) (21.0,37.0) (23.0,31.0) (21.0,37.0)
     | ( 6.0,32.0) (48.0,36.0) (22.0,34.0) (44.0,38.0) | (10.0,30.0) (42.0,34.0) (28.0,36.0) (38.0,36.0)
 0   | (-2.0,26.0) (24.0,38.0) (18.0,26.0) (28.0,36.0) | (-6.0,28.0) ( 6.0,42.0) (16.0,32.0) (26.0,32.0)
     | ( 7.0,29.0) (37.0,39.0) (19.0,33.0) (45.0,35.0) | ( 7.0,29.0) (39.0,33.0) (21.0,37.0) (35.0,35.0)
     | (-2.0,26.0) (24.0,38.0) (10.0,30.0) (24.0,38.0) | ( 2.0,24.0) (22.0,34.0) (16.0,32.0) (18.0,36.0)
     | ( 5.0,25.0) (31.0,37.0) ( 9.0,33.0) (31.0,37.0) | ( 9.0,23.0) (37.0,29.0) (15.0,35.0) (21.0,37.0)
-----|-------------------------------------------------|-------------------------------------------------
     | (-4.0,22.0) (10.0,40.0) ( 0.0,30.0) (10.0,40.0) | (-8.0,24.0) (12.0,34.0) (10.0,30.0) ( 8.0,36.0)
     | (11.0,27.0) (41.0,37.0) (15.0,35.0) (41.0,37.0) | (11.0,27.0) (43.0,31.0) (21.0,37.0) (31.0,37.0)
     | (-1.0,23.0) (25.0,35.0) (11.0,27.0) (17.0,39.0) | (-1.0,23.0) (11.0,37.0) (13.0,31.0) (15.0,35.0)
     | (-3.0,29.0) (23.0,41.0) (13.0,31.0) (27.0,39.0) | (-3.0,29.0) (13.0,41.0) (23.0,31.0) (25.0,35.0)
 1   | ( 1.0,27.0) (31.0,37.0) ( 9.0,33.0) (31.0,37.0) | (-3.0,29.0) (21.0,37.0) (23.0,31.0) (21.0,37.0)
     | ( 4.0,28.0) (38.0,36.0) (20.0,30.0) (34.0,38.0) | ( 4.0,28.0) (28.0,36.0) (22.0,34.0) (28.0,36.0)
     | ( 5.0,25.0) (27.0,39.0) (13.0,31.0) (27.0,39.0) | ( 1.0,27.0) (21.0,37.0) (19.0,33.0) (21.0,37.0)
     | ( 0.0,30.0) (26.0,42.0) (16.0,32.0) (30.0,40.0) | (-8.0,34.0) (20.0,40.0) (26.0,32.0) (28.0,36.0)

Example 3

This example computes C = betaC+alphaBA using a 2 × 2 process grid.

Note:: The imaginary parts of the diagonal elements of a complex Hermitian matrix are assumed to be zero, so you do not have to set these values.

Call Statements and Input

 ORDER = 'R'
 NPROW = 2
 NPCOL = 2
 CALL BLACS_GET(0, 0, ICONTXT)
 CALL BLACS_GRIDINIT(ICONTXT, ORDER, NPROW, NPCOL)
 CALL BLACS_GRIDINFO(ICONTXT, NPROW, NPCOL, MYROW, MYCOL)
 
              SIDE  UPLO   M   N     ALPHA     A  IA  JA   DESC_A   B  IB   JB
               |     |     |   |       |       |   |   |    |       |   |   |
 CALL PZHEMM( 'R' , 'U' , 16 , 8 ,   ALPHA   , A , 1 , 1 , DESC_A , B , 1 , 1 ,
 
              DESC_B    BETA     C  IC  JC   DESC_C
                |         |      |   |   |    |
              DESC_B ,  BETA   , C , 1 , 1 , DESC_C )
 
              ALPHA  =  (1.0, 0.0)
 
              BETA   =  (0.0, 0.0)

	Desc_A	Desc_B	Desc_C
DTYPE_	1	1	1
CTXT_	`icontxt`^(IOBG22)	`icontxt`^(IOBG22)	`icontxt`^(IOBG22)
M_	8	16	16
N_	8	8	8
MB_	2	4	4
NB_	2	2	2
RSRC_	0	0	0
CSRC_	0	0	0
LLD_	See below^(EPSSL22)	See below^(EPSSL22)	See below^(EPSSL22)
Notes: `icontxt` is the output of the BLACS_GRIDINIT call. Each process should set the LLD_ as follows: LLD_A = MAX(1,NUMROC(M_A, MB_A, MYROW, RSRC_A, NPROW)) LLD_B = MAX(1,NUMROC(M_B, MB_B, MYROW, RSRC_B, NPROW)) LLD_C = MAX(1,NUMROC(M_C, MB_C, MYROW, RSRC_C, NPROW)) In this example, LLD_A = 4 on all processes, and LLD_B = LLD_C = 8 on all processes.

Global Hermitian matrix A of order 8 with block size 2 × 2:

B,D               0                         1                        2                         3
     *                                                                                                      *
 0   | ( 0.0, 0.0) (-1.0, 0.0) | (-1.0, 0.0) ( 0.0, 1.0) |( 0.0, 1.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 0.0, 1.0) |
     |      .      ( 1.0, 0.0) | ( 0.0, 1.0) ( 1.0, 2.0) |( 0.0, 1.0) ( 1.0, 2.0) | ( 0.0, 1.0) ( 1.0, 2.0) |
     | ------------------------|-------------------------|------------------------|------------------------ |
 1   |      .           .      | (-1.0, 0.0) (-1.0, 0.0) |( 0.0, 1.0) ( 0.0, 1.0) | ( 1.0, 2.0) ( 0.0, 1.0) |
     |      .           .      |      .      (-1.0, 0.0) |( 1.0, 2.0) ( 1.0, 2.0) | ( 0.0, 1.0) ( 1.0, 2.0) |
     | ------------------------|-------------------------|------------------------|------------------------ |
 2   |      .           .      |      .           .      |(-1.0, 0.0) ( 0.0, 1.0) | ( 0.0, 1.0) ( 0.0, 1.0) |
     |      .           .      |      .           .      |     .      ( 1.0, 0.0) | ( 0.0, 1.0) ( 0.0, 1.0) |
     | ------------------------|-------------------------|------------------------|------------------------ |
 3   |      .           .      |      .           .      |     .           .      | ( 0.0, 0.0) ( 0.0, 1.0) |
     |      .           .      |      .           .      |     .           .      |      .      ( 0.0, 0.0) |
     *                                                                                                      *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for A:

p,q  |                        0                        |                        1
-----|-------------------------------------------------|-------------------------------------------------
     | ( 0.0,  . ) (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0) | (-1.0, 0.0) ( 0.0, 1.0) ( 0.0, 1.0) ( 0.0, 1.0)
     |      .      ( 1.0,  . ) ( 0.0, 1.0) ( 1.0, 2.0) | ( 0.0, 1.0) ( 1.0, 2.0) ( 0.0, 1.0) ( 1.0, 2.0)
 0   |      .           .      (-1.0,  . ) ( 0.0, 1.0) |      .           .      ( 0.0, 1.0) ( 0.0, 1.0)
     |      .           .           .      ( 1.0,  . ) |      .           .      ( 0.0, 1.0) ( 0.0, 1.0)
-----|-------------------------------------------------|-------------------------------------------------
     |      .           .      ( 0.0, 1.0) ( 0.0, 1.0) | (-1.0,  . ) (-1.0, 0.0) ( 1.0, 2.0) ( 0.0, 1.0)
     |      .           .      ( 1.0, 2.0) ( 1.0, 2.0) |      .      (-1.0,  . ) ( 0.0, 1.0) ( 1.0, 2.0)
 1   |      .           .           .           .      |      .           .      ( 0.0,  . ) ( 0.0, 1.0)
     |      .           .           .           .      |      .           .           .      ( 0.0,  . )

Global general 16 × 8 matrix B with block size 4 × 2:

B,D               0                         1                         2                         3
     *                                                                                                       *
     | (-1.0,-3.0) ( 0.0,-2.0) | ( 1.0,-1.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 1.0,-1.0) | (-1.0,-3.0) (-1.0,-3.0) |
     | (-1.0,-3.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 1.0,-1.0) (-1.0,-3.0) | (-1.0,-3.0) ( 1.0,-1.0) |
 0   | ( 1.0,-1.0) ( 1.0,-1.0) | (-1.0,-3.0) ( 0.0,-2.0) | (-1.0,-3.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 0.0,-2.0) |
     | ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) (-1.0,-3.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 0.0,-2.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 1.0,-1.0) | ( 1.0,-1.0) ( 0.0,-2.0) |
     | ( 0.0,-2.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 0.0,-2.0) | (-1.0,-3.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
 1   | ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) (-1.0,-3.0) |
     | ( 0.0,-2.0) ( 0.0,-2.0) | (-1.0,-3.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 1.0,-1.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 1.0,-1.0) |
     | (-1.0,-3.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 1.0,-1.0) |
 2   | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 1.0,-1.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
     | ( 0.0,-2.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) (-1.0,-3.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
     | ------------------------|-------------------------|-------------------------|------------------------ |
     | ( 1.0,-1.0) ( 1.0,-1.0) | (-1.0,-3.0) ( 0.0,-2.0) | (-1.0,-3.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 1.0,-1.0) |
     | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) (-1.0,-3.0) |
 3   | ( 0.0,-2.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) |
     | (-1.0,-3.0) ( 0.0,-2.0) | (-1.0,-3.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 1.0,-1.0) | ( 1.0,-1.0) ( 0.0,-2.0) |
     *                                                                                                       *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁
3    |       |

Local arrays for B:

p,q  |                        0                        |                        1
-----|-------------------------------------------------|-------------------------------------------------
     | (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 1.0,-1.0) | ( 1.0,-1.0) (-1.0,-3.0) (-1.0,-3.0) (-1.0,-3.0)
     | (-1.0,-3.0) (-1.0,-3.0) ( 1.0,-1.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 0.0,-2.0) (-1.0,-3.0) ( 1.0,-1.0)
     | ( 1.0,-1.0) ( 1.0,-1.0) (-1.0,-3.0) ( 0.0,-2.0) | (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0)
     | ( 0.0,-2.0) (-1.0,-3.0) ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) (-1.0,-3.0)
 0   | ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0)
     | (-1.0,-3.0) (-1.0,-3.0) ( 0.0,-2.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0)
     | ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0)
     | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0)
-----|-------------------------------------------------|-------------------------------------------------
     | ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 1.0,-1.0) ( 1.0,-1.0) ( 0.0,-2.0)
     | ( 0.0,-2.0) ( 0.0,-2.0) (-1.0,-3.0) (-1.0,-3.0) | ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0)
     | ( 1.0,-1.0) ( 1.0,-1.0) ( 1.0,-1.0) ( 1.0,-1.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) (-1.0,-3.0)
     | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0) | (-1.0,-3.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0)
 1   | ( 1.0,-1.0) ( 1.0,-1.0) (-1.0,-3.0) (-1.0,-3.0) | (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 1.0,-1.0)
     | ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) (-1.0,-3.0)
     | ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0) ( 0.0,-2.0) | ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 0.0,-2.0)
     | (-1.0,-3.0) ( 0.0,-2.0) ( 0.0,-2.0) ( 1.0,-1.0) | (-1.0,-3.0) ( 0.0,-2.0) ( 1.0,-1.0) ( 0.0,-2.0)

Output:

Global general 16 × 8 matrix C with block size 4 × 2:

B,D               0                          1                         2                         3
     *                                                                                                        *
     | (-12.0,4.0) (-19.0,-5.0) | (-9.0, 5.0) (-5.0,-5.0) | ( 3.0,-3.0) ( 9.0,-5.0) | (10.0, 2.0) (18.0,-6.0) |
     | (-10.0,4.0) (-17.0,-7.0) | (-9.0, 3.0) (-5.0,-9.0) | ( 3.0,-1.0) ( 9.0,-9.0) | (14.0,-2.0) (20.0,-8.0) |
 0   | (-10.0,4.0) (-19.0,-5.0) | (-7.0, 5.0) (-11.0,1.0) | ( 5.0, 1.0) (11.0,-5.0) | (12.0,-4.0) (17.0,-1.0) |
     | (-10.0,6.0) (-22.0,-6.0) | (-8.0, 4.0) (-10.0,-6.0)| ( 4.0, 0.0) (10.0,-8.0) | (12.0,-2.0) (19.0,-7.0) |
     | -------------------------|-------------------------|-------------------------|------------------------ |
     | (-8.0, 0.0) (-10.0,-8.0) | (-6.0, 2.0) (-6.0,-4.0) | ( 4.0, 2.0) (10.0, 0.0) | ( 9.0, 1.0) (14.0, 4.0) |
     | (-13.0,5.0) (-21.0,-5.0) | (-11.0,5.0) (-15.0,-3.0)| ( 3.0, 3.0) ( 9.0,-7.0) | (13.0,-1.0) (19.0,-5.0) |
 1   | (-10.0,2.0) (-17.0,-7.0) | (-9.0, 3.0) (-7.0,-1.0) | ( 1.0, 1.0) ( 7.0, 1.0) | ( 7.0, 3.0) (14.0, 2.0) |
     | (-7.0, 3.0) (-13.0,-7.0) | (-5.0, 3.0) (-1.0,-5.0) | ( 7.0,-3.0) (13.0,-7.0) | (13.0,-5.0) (18.0,-4.0) |
     | -------------------------|-------------------------|-------------------------|------------------------ |
     | (-8.0, 2.0) (-14.0,-8.0) | (-4.0, 2.0) ( 2.0,-6.0) | ( 6.0,-6.0) (12.0,-8.0) | (12.0,-2.0) (17.0,-5.0) |
     | (-10.0,4.0) (-17.0,-7.0) | (-7.0, 3.0) (-7.0,-9.0) | ( 5.0,-1.0) (11.0,-11.0)| (15.0,-3.0) (20.0,-8.0) |
 2   | (-8.0, 2.0) (-14.0,-8.0) | (-8.0, 2.0) (-6.0,-6.0) | ( 2.0, 2.0) ( 8.0,-2.0) | (10.0, 0.0) (16.0, 0.0) |
     | (-11.0,3.0) (-17.0,-7.0) | (-11.0,3.0) (-13.0,-5.0)| ( 1.0, 5.0) ( 7.0,-3.0) | (11.0, 1.0) (17.0,-1.0) |
     | -------------------------|-------------------------|-------------------------|------------------------ |
     | (-10.0,4.0) (-19.0,-5.0) | (-7.0, 5.0) (-11.0,1.0) | ( 5.0, 1.0) (11.0,-7.0) | (14.0,-6.0) (18.0,-2.0) |
     | (-10.0,4.0) (-20.0,-6.0) | (-8.0, 4.0) (-8.0,-4.0) | ( 2.0, 0.0) ( 8.0,-4.0) | (10.0, 0.0) (17.0,-3.0) |
 3   | (-11.0,3.0) (-17.0,-5.0) | (-9.0, 5.0) (-9.0,-1.0) | ( 3.0, 1.0) ( 9.0,-3.0) | (11.0,-1.0) (17.0,-1.0) |
     | (-7.0, 3.0) (-14.0,-6.0) | (-2.0, 4.0) (-2.0,-6.0) | ( 8.0,-4.0) (14.0,-8.0) | (13.0,-5.0) (18.0,-4.0) |
     *                                                                                                        *

The following is the 2 × 2 process grid:

B,D  |  0 2  |1 3
-----|-------|-----
0    |   P₀₀   |  P₀₁
2    |       |
-----|-------|-----
1    |   P₁₀   |  P₁₁3    |       |

Local arrays for C:

p,q  |                            0                            |                            1
-----|---------------------------------------------------------|---------------------------------------------------------
     | (-12.0,  4.0) (-19.0, -5.0) (  3.0, -3.0) (  9.0, -5.0) | ( -9.0,  5.0) ( -5.0, -5.0) ( 10.0,  2.0) ( 18.0, -6.0)
     | (-10.0,  4.0) (-17.0, -7.0) (  3.0, -1.0) (  9.0, -9.0) | ( -9.0,  3.0) ( -5.0, -9.0) ( 14.0, -2.0) ( 20.0, -8.0)
     | (-10.0,  4.0) (-19.0, -5.0) (  5.0,  1.0) ( 11.0, -5.0) | ( -7.0,  5.0) (-11.0,  1.0) ( 12.0, -4.0) ( 17.0, -1.0)
     | (-10.0,  6.0) (-22.0, -6.0) (  4.0,  0.0) ( 10.0, -8.0) | ( -8.0,  4.0) (-10.0, -6.0) ( 12.0, -2.0) ( 19.0, -7.0)
 0   | ( -8.0,  2.0) (-14.0, -8.0) (  6.0, -6.0) ( 12.0, -8.0) | ( -4.0,  2.0) (  2.0, -6.0) ( 12.0, -2.0) ( 17.0, -5.0)
     | (-10.0,  4.0) (-17.0, -7.0) (  5.0, -1.0) ( 11.0,-11.0) | ( -7.0,  3.0) ( -7.0, -9.0) ( 15.0, -3.0) ( 20.0, -8.0)
     | ( -8.0,  2.0) (-14.0, -8.0) (  2.0,  2.0) (  8.0, -2.0) | ( -8.0,  2.0) ( -6.0, -6.0) ( 10.0,  0.0) ( 16.0,  0.0)
     | (-11.0,  3.0) (-17.0, -7.0) (  1.0,  5.0) (  7.0, -3.0) | (-11.0,  3.0) (-13.0, -5.0) ( 11.0,  1.0) ( 17.0, -1.0)
-----|---------------------------------------------------------|---------------------------------------------------------
     | ( -8.0,  0.0) (-10.0, -8.0) (  4.0,  2.0) ( 10.0,  0.0) | ( -6.0,  2.0) ( -6.0, -4.0) (  9.0,  1.0) ( 14.0,  4.0)
     | (-13.0,  5.0) (-21.0, -5.0) (  3.0,  3.0) (  9.0, -7.0) | (-11.0,  5.0) (-15.0, -3.0) ( 13.0, -1.0) ( 19.0, -5.0)
     | (-10.0,  2.0) (-17.0, -7.0) (  1.0,  1.0) (  7.0,  1.0) | ( -9.0,  3.0) ( -7.0, -1.0) (  7.0,  3.0) ( 14.0,  2.0)
     | ( -7.0,  3.0) (-13.0, -7.0) (  7.0, -3.0) ( 13.0, -7.0) | ( -5.0,  3.0) ( -1.0, -5.0) ( 13.0, -5.0) ( 18.0, -4.0)
 1   | (-10.0,  4.0) (-19.0, -5.0) (  5.0,  1.0) ( 11.0, -7.0) | ( -7.0,  5.0) (-11.0,  1.0) ( 14.0, -6.0) ( 18.0, -2.0)
     | (-10.0,  4.0) (-20.0, -6.0) (  2.0,  0.0) (  8.0, -4.0) | ( -8.0,  4.0) ( -8.0, -4.0) ( 10.0,  0.0) ( 17.0, -3.0)
     | (-11.0,  3.0) (-17.0, -5.0) (  3.0,  1.0) (  9.0, -3.0) | ( -9.0,  5.0) ( -9.0, -1.0) ( 11.0, -1.0) ( 17.0, -1.0)
     | ( -7.0,  3.0) (-14.0, -6.0) (  8.0, -4.0) ( 14.0, -8.0) | ( -2.0,  4.0) ( -2.0, -6.0) ( 13.0, -5.0) ( 18.0, -4.0)

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Parallel Engineering and Scientific Subroutine Library for AIX Version 2 Release 3: Guide and Reference

PDSYMM, PZSYMM, and PZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian

Syntax

On Entry

On Return

Notes and Coding Rules

Error Conditions

Computational Errors

Resource Errors

Input-Argument and Miscellaneous Errors

Example 1

Call Statements and Input

Example 2

Call Statements and Input

Example 3

Call Statements and Input