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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine sggsvp | ( | character | JOBU, |
character | JOBV, | ||
character | JOBQ, | ||
integer | M, | ||
integer | P, | ||
integer | N, | ||
real, dimension( lda, * ) | A, | ||
integer | LDA, | ||
real, dimension( ldb, * ) | B, | ||
integer | LDB, | ||
real | TOLA, | ||
real | TOLB, | ||
integer | K, | ||
integer | L, | ||
real, dimension( ldu, * ) | U, | ||
integer | LDU, | ||
real, dimension( ldv, * ) | V, | ||
integer | LDV, | ||
real, dimension( ldq, * ) | Q, | ||
integer | LDQ, | ||
integer, dimension( * ) | IWORK, | ||
real, dimension( * ) | TAU, | ||
real, dimension( * ) | WORK, | ||
integer | INFO | ||
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SGGSVP
Download SGGSVP + dependencies [TGZ] [ZIP] [TXT]
This routine is deprecated and has been replaced by routine SGGSVP3. SGGSVP computes orthogonal matrices U, V and Q such that N-K-L K L U**T*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0; L ( 0 0 A23 ) M-K-L ( 0 0 0 ) N-K-L K L = K ( 0 A12 A13 ) if M-K-L < 0; M-K ( 0 0 A23 ) N-K-L K L V**T*B*Q = L ( 0 0 B13 ) P-L ( 0 0 0 ) where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T. This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine SGGSVD.
[in] | JOBU | JOBU is CHARACTER*1 = 'U': Orthogonal matrix U is computed; = 'N': U is not computed. |
[in] | JOBV | JOBV is CHARACTER*1 = 'V': Orthogonal matrix V is computed; = 'N': V is not computed. |
[in] | JOBQ | JOBQ is CHARACTER*1 = 'Q': Orthogonal matrix Q is computed; = 'N': Q is not computed. |
[in] | M | M is INTEGER The number of rows of the matrix A. M >= 0. |
[in] | P | P is INTEGER The number of rows of the matrix B. P >= 0. |
[in] | N | N is INTEGER The number of columns of the matrices A and B. N >= 0. |
[in,out] | A | A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section. |
[in] | LDA | LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). |
[in,out] | B | B is REAL array, dimension (LDB,N) On entry, the P-by-N matrix B. On exit, B contains the triangular matrix described in the Purpose section. |
[in] | LDB | LDB is INTEGER The leading dimension of the array B. LDB >= max(1,P). |
[in] | TOLA | TOLA is REAL |
[in] | TOLB | TOLB is REAL TOLA and TOLB are the thresholds to determine the effective numerical rank of matrix B and a subblock of A. Generally, they are set to TOLA = MAX(M,N)*norm(A)*MACHEPS, TOLB = MAX(P,N)*norm(B)*MACHEPS. The size of TOLA and TOLB may affect the size of backward errors of the decomposition. |
[out] | K | K is INTEGER |
[out] | L | L is INTEGER On exit, K and L specify the dimension of the subblocks described in Purpose section. K + L = effective numerical rank of (A**T,B**T)**T. |
[out] | U | U is REAL array, dimension (LDU,M) If JOBU = 'U', U contains the orthogonal matrix U. If JOBU = 'N', U is not referenced. |
[in] | LDU | LDU is INTEGER The leading dimension of the array U. LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise. |
[out] | V | V is REAL array, dimension (LDV,P) If JOBV = 'V', V contains the orthogonal matrix V. If JOBV = 'N', V is not referenced. |
[in] | LDV | LDV is INTEGER The leading dimension of the array V. LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise. |
[out] | Q | Q is REAL array, dimension (LDQ,N) If JOBQ = 'Q', Q contains the orthogonal matrix Q. If JOBQ = 'N', Q is not referenced. |
[in] | LDQ | LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise. |
[out] | IWORK | IWORK is INTEGER array, dimension (N) |
[out] | TAU | TAU is REAL array, dimension (N) |
[out] | WORK | WORK is REAL array, dimension (max(3*N,M,P)) |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. |
Definition at line 258 of file sggsvp.f.