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

DBSTRS--Symmetric Indefinite Matrix Multiple Right-Hand Side Solve

The DBSTRS subroutine solves a system of linear equations AX = B for X, where A is a real symmetric indefinite matrix, and X and B are real general matrices. This subroutine uses the results of the factorization of matrix A, produced by a preceding call to DBSTRF.

Table 99. Data Types

Note:

The input to this solve subroutine must be the output from the factorization subroutine DBSTRF.

Syntax

On Entry

uplo

indicates whether original matrix A is stored in upper- or lower-packed storage mode, where:

If uplo = 'U', A is stored in upper-packed storage mode.

If uplo = 'L', A is stored in lower-packed storage mode.

Specified as: a single character. It must be 'U' or 'L'.

n

is the order n of factored matrix A and the number of rows of matrix B.

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

nrhs

is the number of right-hand sides; i.e., the number of columns of matrix B.

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

ap

is the factored matrix A produced by a preceding call to DBSTRF.

Specified as: a one-dimensional array of length nsinfo, containing numbers of the data type indicated in Table 99. See Notes and DBSTRF--Symmetric Indefinite Matrix Factorization.

ipvt

is an integer vector of length n, containing the pivot information necessary to construct the factored form of A, produced by a preceding call to DBSTRF..

Specified as: a one-dimensional array of (at least) length n, containing numbers of the data type indicated in Table 99. See Notes.

b

is the matrix B, containing the nrhs right-hand sides of the system. The right-hand sides, each of length n, reside in the columns of matrix B.

Specified as: an ldb by (at least) nrhs array, containing numbers of the data type indicated in Table 99.

ldb

is the leading dimension of the array specified for B.

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

info

See On Return.

On Return

b

is the matrix B, containing the nrhs solutions to the system in the columns of B.

Returned as: an ldb by (at least) nrhs array, containing numbers of the data type indicated in Table 99.

info

indicates the result of the computation.

• If info = 0, the subroutine completed successfully.

Returned as: a fullword integer.

Notes

1. This subroutine accepts lowercase letters for the uplo argument.
2. In your C program, argument info must be passed by reference.
3. The array data specified for input arguments ap and ipvt for this subroutine must be the same as the corresponding output arguments for DBSTRF.
4. The scalar data specified for input arguments uplo and n must be the same as that specified for DBSTRF.
5. The vectors and matrices used in this computation must have no common elements; otherwise, results are unpredictable. See Concepts.
6. For a description of how a symmetric matrix is stored in upper- or lower-packed storage mode in an array, see Symmetric Matrix.
7. To solve AX = B for X, where B and X are n by nrhs matrices, precede the call to DBSTRS with a call to DBSTRF.

Function

The system AX = B is solved for X, where A is a real symmetric indefinite matrix, and X and B are real general matrices. This subroutine uses the results of the factorization of matrix A, produced by a preceding call to DBSTRF.

If n or nrhs is 0, no computation is performed and the subroutine returns after doing some parameter checking.

See references [8] and [65].

Error Conditions

Resource Errors

None.

Computational Errors

None.

Note:

If the factorization performed by DBSTRF failed because matrix A is singular, the results returned by this subroutine are unpredictable, and there may be a divide-by-zero program exception message.

Input-Argument Errors

1. uplo <> 'U' or 'L'
2. n < 0
3. nrhs < 0
4. n > ldb
5. ldb <= 0

Example 1

This example shows how to solve the system AX = B, for three right-hand sides, where matrix A is the same matrix factored in the Example 1 for DBSTRF.

Call Statement and Input

              UPLO  N   NRHS  AP  IPVT  B  LDB  INFO
               |    |    |     |   |    |   |     |
CALL DBSTRS ( 'L',  8,   3,   AP, IPVT, B,  8,  INFO )

        *                     *
        |   1.0  -38.0   47.0 |
        |   7.0  -10.0   73.0 |
        |   6.0   52.0    2.0 |
B    =  | -30.0 -228.0  -42.0 |
        |  32.0  183.0  105.0 |
        |  34.0  297.0    9.0 |
        |  32.0  244.0   44.0 |
        |  62.0  497.0   61.0 |
        *                     *

Output

        *                     *
        |   1.0    1.0    8.0 |
        |   1.0    2.0    7.0 |
        |   1.0    3.0    6.0 |
B    =  |   1.0    4.0    5.0 |
        |   1.0    5.0    4.0 |
        |   1.0    6.0    3.0 |
        |   1.0    7.0    2.0 |
        |   1.0    8.0    1.0 |
        *                     *

INFO = 0

Example 2

This example shows how to solve the system AX = B, for three right-hand sides, where matrix A is the same matrix factored in the Example 2 for DBSTRF.

Call Statement and Input

              UPLO  N   NRHS  AP  IPVT  B  LDB  INFO
               |    |    |     |   |    |   |     |
CALL DBSTRS ( 'U',  8,   3,   AP, IPVT, B,  8,  INFO )

        *                     *
        |  59.0   52.0  479.0 |
        |  30.0   38.0  232.0 |
        |  33.0   50.0  247.0 |
B    =  |  35.0  114.0  201.0 |
        | -28.0  -36.0 -216.0 |
        |   4.0   -4.0   40.0 |
        |  12.0   88.0   20.0 |
        |   4.0   56.0  -20.0 |
        *                     *

Output

        *                     *
        |   1.0    1.0    8.0 |
        |   1.0    2.0    7.0 |
        |   1.0    3.0    6.0 |
B    =  |   1.0    4.0    5.0 |
        |   1.0    5.0    4.0 |
        |   1.0    6.0    3.0 |
        |   1.0    7.0    2.0 |
        |   1.0    8.0    1.0 |
        *                     *

INFO = 0